I'm going to make this simple. It has been scientifically proven that negative comments affect somebody's mindset, and constant harassment worsens these effects. In a game of LoL, being constantly told "you're shit," "uninstall," etc. WILL make you feel that way, even if just slightly. If you have a few bad games and hear it a lot, it only gets worse. Additionally, people with a history of depression (maybe not even due to words or people being assholes) are more psychologically vulnerable, and very little hate towards them can set them off whether they like it or not. People don't choose to be offended. And it's not because they're "weaker" than you.
Imagine this scenario: A kid is being horribly abused by his parents. Every day, they yell at him and tell him how worthless he is. If he tries to escape, they threaten him. Now, in MOST CASES of adult depression, childhood abuse is a factor, thus depression would come from this. Would you call them weak? Would you call them a mewling infant because their parents treated them like shit? I doubt it. And this is just like that on a MUCH SMALLER LEVEL. I'm not directly comparing assholes in League to abusive parents.
Here's an analogy: Abusive Parents are to Depression as League Assholes are to Annoyance/Tilt/Being Offended. In neither case can you call the person "weak," or "small-minded," as it is a scientific fact that their mindset will be affected.
Maybe instead of basing your argument around calling people pansies and accusing them of needing a safe space or cry closet, you should engage in logical, unbiased arguments supported by fact. That's my argument, and if you don't agree with me, that's ok, debate with people elsewhere. The LoL boards aren't for this kind of thing.