I think I have become a shitty human being

That being said. Openly berating someone for not being able to do a task is a bitch move. He can't do the job and he doesn't belong there but he doesn't need you screaming in his face about it. That type of attitude can and will bite you in the ass later.

I've worked for the yelling and screaming type of chefs before. They're gone and I'm still here.

You really do seem like a piece of shit for the way you treated him. You even said it was public funds and were required to have him around. The fact that it was someone else's money and efficiency didn't seem to be the top priority for them means you probably got some sort of pleasure out of the way you treated him. Then rationalizing it as ok because you're only 24 screams personality disorder