See, heres the thing. As I’m sure you know, UA, and many other hero schools, start training students when they’re only 15/16. That’s really young. Their brains are hardly developed, and they haven’t been exposed to much of larger society. Most of what they’ve seen of heroes is the glorified, sugarcoated version.

Not to mention, at least some of the students have been coddled, told they’d be amazing heroes, etc, and this inevitably will affect their personality and ego. I mean, just look at Bakugou.

Now. To be honest, I don’t really think Aizawa is that extreme. See, the thing is, being a hero is not all fun and games, not in the slightest. And Aizawa knows this. A simple sit down about the dangers of being a hero, and its high risk of death (particularly for younger, more reckless individuals) isn’t effective enough for those thick headed students that this method is mostly intended for. Expulsion the closest thing to ‘death’ he can give those students who, intentionally or no, have a death wish from being so reckless. 

Midoriya is actually a great example of the mindset Aizawa is trying to discourage. Midoriya doesn’t seem to have much of a self preservation instinct. He doesn’t care what happens to him, and that’s a problem. Even only a few months into being a hero student, he’s at risk of a forced retirement from how badly he’s damaged himself, and It’s this self sabotaging, over reckless mindset that Aizawa is trying to prevent.