It doesn't take a rocket scientist to write a movie if you have the passion, determination, you'll do it. The best directors working today didn't even go to college.. Hell, Tarantino.. didn't even make it to high school and basically learned by watching films and reading George V Higgins and Elmore Leonard books..
Two huge misconceptions in your post.
1) It's not rocket science to write a script.
It might not be rocket science to write one but its really fukking hard to write one that's worth a shyt. There are about 10 full time working go-to screenwriters in The industry and a 100 who get regular work.
That's not because Hollywood is exclusive. That's because writing screenplays is extremely hard.
Side-note: Sure there are directors working who didn't do the IVY league, USC or NYU thing. But they are extremely extremely lucky. The point of film school is to make connections and network. The education you get there can be had for nothing. But the exposure and contacts are priceless.
I will say this protect your shyt if you do finish it... because there are shytload of people (especially established people in Hollywood) who love to steal shyt. They will steal your screenplay or small indy flick and rename it, while changing minor things, etc..
2) someone is going to steal your screenplay
No one is going to steal your screenplay. Chances are if you wrote it, regardless of how original you think it is, that same idea is already out there floating around to begin with. Every few years you'll get a friviolous lawsuit thrown out by a judge for this reason. It's actually cheaper for the studios to simply buy your script at bottom rate than it would be for them to defend the lawsuit.
Sure someone might steal the way you did something, an approach you took, a ticking time bomb or an obstacle. But that's common. Most writers read other writers' scripts and sub consciously or consciously steal shyt all of the time.
Registering your script is the best bet and a good step, but don't be afraid to have others look at your work.