Barney did not get fired. In fact, there isn’t any news that he got fired. David Joyner, the Barney of the era, probably just willingly retired from the job. It’s easy to create rumors around a grown adult black man, role-playing in a purple dinosaur suit, surrounded by children. Because Barney was such a huge symbol to the kids, any rumor that the parents caught on is a warning to them. In fact, all the children’s show hosts have always been the target for terrible rumors. Steve of Blues Clue’s never died from a heroin overdose (he is still alive and well today). Mr. Rogers of Mister Roger’s Neighborhood was never a convicted child molester. Similarly, there was never a drug bust done of the Barney & Friends set, the actor was never a child molester (although he really does love role-playing as anthropomorphic animals) and there was never any evidence that he curses in front of live audiences. It’s just baseless rumor made to create conspiracies, just because Barney was an easy target. Not that it doesn’t happen, with the Bill Cosby sexual “allegations” being major news. So it’s not really difficult to see why these children’s symbols are attacked.
With that being said, why did he quit then? It’s simple really, probably due to exhaustion from the job. David Joyner played the same character for 8 consecutive years. No matter how enthusiastic you are, bouncing around, dancing in the same heavy costume, doing that long enough and you will probably get tired of it. Not to mention all the rumors spreading around probably didn’t motivate him mentally. That is why David Joyner resigned his role as Barney. He only joined another troupe, playing in another anthropomorphic costume, as Hip Hop Harry, 6 years later. So if you ask why did Barney get fired, the fact is Barney did not get fired, but simply needing a long break.