The Mad King didn't get that title because he was a killer or a tyrant. Who has killed more people than Tywin Lannister? Buddy wiped out two noble houses from the face of the earth, even had a hit single made to commemorate it. He facilitated the brutal sacking and pillaging of King's Landing, and had his forces commit numerous atrocities during the war with Robb Stark. And yet he was never considered mad. Wake me up when Dany is tortured for weeks in a dungeon while thinking her best friend abandoned her, starts having debilitating visual and auditory hallucinations, and begins to believe that everyone around her is plotting to destroy her. That's the things that made Aerys II be known as the Mad King.
It's beyond annoying that every time Dany goes "boo," people immediately start going on about "Mad King this, Mad King that." The dude was literally crazy and there were multiple things that happened to him that caused that; one of which was being an idiot and ignoring Tywin's pleading to not parly with a lord who refused orders from the crown. Ended up getting his ass thrown in a cellar.