The movie does actually stick to classical timespace continuum and laws of physics / relativity spot on, you just happened to not see it because it takes place before the movie. But: the movie is full of hints of the original events (the rooster, purpose, trancendence of the inevidable destiny no matter how much you change spacetime).
Before the paradox (call this iteration/loop 0), the child has a natural mother and father, and does not live in an orphanage. The child does have the dualsex anomaly though, and is raised as a boy/man having most visible traits of a male specimen.
The boy grows up to be a man, starts working for SpaceCorp as an agent, travels back in time doing missions, but starts doing it too much, gets disoriented / psychotic, and starts a relationship with his own natural (in iteration 0 before the paradox) unparadoxed mother (denmark-syndrome). He impregnates her, and at the time his sperm fertilizes her egg he ceases to exist in the original "version" - a paradox takes place and we are now in an alternate timeline (iteration 1), he will immidiatly become different.
The natural mother now never meets the original father, the child now is his own father, but not yet his own mother, child grows up - this time grown up as a girl, the older version from (iteration 1) travels back in time and starts a relationship with his younger girl-self iteration-2 (reversed denmark-syndrome), in which he - feeling guilty - kidnaps the baby (which no longer is a product of his natural mother/father, but the product of himself purely on both sides) in regret of the whole mess, so he tries to travel back to a totally different time (1945) to leave his baby-self at an unknown orphanage in hopes of making the paradox stop.
Now the movie starts, the rest you've seen. The rooster and the orphanage is the best clues that there is "something" before the whole chicken-and-the-egg paradoxial situation, namely the roosters "cum" which is the natural events before the paradox leading up to triggering the singularity of the endless loops. And the orphanage: There is no other reason for him to leave the child at an orphanage, other than to try to stop a mess he himself has made and feels regret about
It's only after the movie starts and the paradox has allready taken place that he continues to place the baby there each loop simply because if he doesnt continue to do so,he will cease to exist since he now longer is the product of a natural mother/father, but merely a product of two timetravel-imposed iterations of himself. From that point on if he doesn't continue to work as an agent, fails to deliver the baby, or fail to impregnate himself, he will stop existing alltogether.
PS: All the iterations/loops happens in rapid increasing exponential curve / as an infinite singularity event, so only the individuals caught in the loop will percieve it as "linear in time" but it all happens simultaniously when the paradox is triggered (when going from iteration 0 -> 1), like an event horizon: after that point there is no return from that paradox, and it's impossible to stop the loop by any means. Any attempt to kill the younger version will immediatly eradicate the older version who initially attempted to kill the younger version and so fourth, making any means - both non lethal or lethal to stop the iterations impossible.
Also, the first event at iteration 0, where he goes back to impregnate his own first natural mother isnt by coincidence, this is the actual experiment imposed by spaceCorp's mr. Robertson, to proove/disprove a number of theories they want to put to the test:
A: that its actually possible to create a paradoxal version of yourself with no possible return to your normal natural-born state.
B: Will the conciousness of the timetraveller survive the iterations / new alternate timelines, and
C: will two different beings (alternate versions of yourself) with similar destinies make the same choices (since john/jane from iteration 0 is actually a different person than john/jane from iteration 1,2 and any later iteration). Each iteration there is a new spermcell from a new iteration-version of himself impregnating a new egg in a new version of herself endlessly, meaning john/jane is actually a "cloned" individual when a new alternate timeline is created and the current john/jane ceases to exist along with the current timeline that was just alternated. (almost like in the movie "The prestige", he never teleports, he gets "cloned" by time&space itself, but in that movie he needs to kill of the "original" every time himself by force since the teleport is in reality a timetravel-device, but the time he travels is less than a second, so he ends up with two versions of himself in the same timeline, one original, and one timetraveller who traveled one second into the future). In that sense there are no real clones, both are actually the original, but from different timelines.
The movie could have just done that to make it easy to understand that all iterations of john/jane are the "original", but from different alternate timelines/realitites, but they chose to complicate it with putting in the impregnation/child into the mix.
spaceCorp wants to find out if their conciosness is somehow transferred into the new iterated version, if so - it is proof that conciousness/"soul" and even purpose is reincarnatable into new specimens and that they are not bound by timespace continuum.
spaceCorp is there the whole time in the background "pushing" in jane/john down a certain path making sure the experiment goes the way it should be in terms of events enforced by Mr. Robertson giving him "missions" all the time, which in reality are incentives. The bombings are just a sideeffect of jane/johns versions developing a psychosis due to all these strange / looped and paradoxial events, in which spaceCorp quickly uses as a bait to make sure jane/john stays on the path of conducting the experiment, which is also hinted throughout the movie "We have learned so much from the Fizzle bomber, and we wouldn't have been where we're at without him".
The movie could offcourse have included iteration 0 in the beginning, but then it would have become too clear what is actually happening and why, leaving out all the fun and thought for the viewer to ponder about afterwards, so instead it gives it away as subtle clues, which i favor over getting it "spelled out" in front of me in a patronizing way underestemating the intelligence of the viewer.
If i want movies / plots that are allready pre-drawn with the lines in the "connect the dots" I would go watch CSI,NCIS,NCSI,CSINCI florida, CSINICY washington or any tv-show with real peopl.. teenage-actors on ADHD-TV (disney XD, nick, cartoon network etc.)
This movie leaves most by subtle hints only to be discovered, which is what makes it intelligent and makes it a good watch, and will make me want to watch it again just to look for more clues and cameo hints. The movie relies on the hints and the plot instead of a 600.000.000 trillion FX-hollywood blockbuster budget, and would therefore probarbly bore the hell out of a 12-year old, which (imo) is a good thing.
ETA: Ending explanation
What I meant by explicate the ending, is that you must try to consider Fizzle Bomber as the merging of all different 'states' of his being into one. Fizzle Bomber IS the culmination/beginning of the entire ordeal. Fizzle Bomber is the last piece of domino in the chain, which is predestined to fall and cause the fall of the first domino in the chain. As Fizzle Bomber dies(last domino), Fizzle Bomber is created(first domino) out of John, sustaining the succession of events to basically start over in it's new cycle.
In my opinion, beyond the whole paradox thing, this movie is actually a rather poetic, beautiful tragic love story. The paradox is the premise, but what truly makes this movie compelling, in my opinion, is that through the transgender/self-love twists, this movie not only illustrates well the Predestination Paradox, it gives acomplex portrayal of an emotional strange loop so strong that it "Can't be paradoctored."
Purpose, Love and Hatred are the driving themes of this movie, time travel is only the premise.
I'll discuss the final scene and ending in (Spoilers): John: The snake that eats it's own tail.. Forever and ever.
It'll help if you understand that Fizzle Bomber acts out of absolute love for John/Jane. To simplify this, instead of seeing Ethan Hawke as the Fizzle Bomber, try to envision the face of Sarah Snook as the Fizzle Bomber. To simplify further, let's just call Fizzle Bomber Jane, and the one confronting him John.
Fizzle Bomber/Jane is desperately in love with John, but John is desperately driven by a desire to avenge Jane/John's suffering by murdering Fizzle Bomber.
When Older John meets Younger Jane in the park and they fall in love, John recognizes Jane, but Jane is unable to recognize John. The way the final scene is orchestrated, it's virtually the opposite of that encounter. Consider that Fizzle Bomber is an Older Jane finally being reunited with a Younger John, but this time, only Jane can recognize John, and John is unable to recognize Jane inside the Fizzle Bomber.
Jane/John's incredible love for John/Jane and John/Jane's incredible hatred for Fizzle Bomber/Jane/John is the essence of the loop, the moving force which sets every event in motion over and over.
So, understood as such, the final scene is a very poignant tragic love reunion of two lovers who are destined to always be blind-sided to 'the other'.
The final confrontation is a scene where both parties confess their emotions. Fizzle Bomber/Jane/John is confessing her utter love for John/Jane/Fizzle Bomber, while John/Jane/Fizzle Bomber is confessing his utter hatred for Fizzle Bomber/Jane/John.
Changing the name/faces in the script will help illustrate and I hope appreciate this:
[John enters the Laundrymat]
Jane: Oh my god.. You look good.. I missed you.
John: ..You're the Fizzle Bomber?
Jane: [Laughs] We always hated that name, remember?
John: [Astonished] ..You're a murderer.
Jane: ..You're disappointed in me, right? I remember that, I do. But when the dust settles.. I think you'll see that we did the right thing.
John: I will never become you.
Jane: Some people say that it's fate. But you and I, we know, some things are predestined. I made you who you are, you made me who I am. It's a paradox, right? But it can't be.. paradoctored. [Psychotic laughter]
Jane: [Overjoyed] And now you're free and you found me and we can finally be together!
John: .. I'll never become you.
Jane: Don't say that. Don't say that.
John: .. I will never become you and I will not let you kill those people!
Jane: [Angry/Feeling Betrayed] Wait Wait Wait, What, you're gonna live a regular life, with that bytch, Alice, from the antique store? She has a stupid cat, she has a disgusting birthmark on her left hip, she's a lousy *beep* cook! Okay trust me, she can't handle our secrets! She can't, trust me! She's not right for us!
John: You have no idea what is right for me!
Jane: Okay, okay, listen. All we have is each other. It is ALL we've ever had. Now, if you shoot me.. You'll become me. You get it? That's.. how it happens. If you want to break the chain, you have to not kill me.. But try.. To love me.. Again..
John: [Tearing Up]..What if I put him in front of you.. ..The man who ruined your life..
Jane: Yeah yeah yeah... Forget all that. We can have a future together.
John: ..Would you kill him.. To save thousands?
Jane: ... You wanna know what we're gonna do tomorrow? [Excited]
John: [Breaking Down] No.
[Gunshots/Death and Rebirth of Fizzle Bomber/Beginning of a new cycle in the loop]
[A Younger John listens to a tape recorded by the new cycle Fizzle Bomber/Jane at the beginning of his career as a TTA]
New Cycle Fizzle Bomber/Jane: [Talking to a Younger John through a recording] Here you are.. At the beginning of your new life. It can be overwhelming, knowing the future you're about to create.. Knowing the purpose of that life. You know who she is. and you understand who you are. And now maybe you're ready to understand who I am.. You see I.. I love her too. You'll have to make tough choices. You'll influence the past. Can we change our futures? I.. I don't know.The only thing that I know for sure.. ..Is that you are the best thing that's ever happened to me. I miss you dreadfully