People are tired from crybullies. We need a place where freedom of speech still matters. Freedom of speech doesn't include invading someone's privacy (this is illegal; doxxing, stalking etc. should be banned and actively fought against). But if you can't handle insults, it is not anyone's job to prevent them. There's always "Block" button, and then, there's always "delete account" button.
First, I don't think you speak for "People," just the kind of people who are just like you. For example, I have never used the expression "crybullies," and if I did, it would probably be to describe the kind of white male who gets on a place like HN and cries that his freedom to be a raging asshole in somebody else's privately owned medium is being trampled by moderation. But back to your point, I will argue with it…
Of course, just like you do and everybody else is doing. Therefore, my opinion is just my opinion, and if somebody insults me, it is their opinion, and I am not obliged to react to it in any way. I might, if it would be someone I know and respect, but an anonymous account created two weeks ago just to post a random insult in my direction? I'd be flattered I am _that_ important for somebody.
And as you have just said, Twitter is a private company. They can serve needs of people like you or people like me (and I do not engage in insults, this is immature — but I do value freedom of speech and its total independence from the current PC handbook du jour). The question is what is more profitable and what is more aligned with founder's values.