Well, in her bad ending, she's doing something that she does yearly, and that is shutting out everyone that seems to matter to her, including the guy she's mutually crushing on. Hisao in the neutral ending handles it a lot better, but so does Hanako in that one.
The issue there is that her behavior is something to worry about. It's not the norm, it's unusual, it's frightening for the people that care about her. It makes people think that leaving her alone is going to be a very terrible idea.
I realize it's stressful to be treated that way, but for an someone else looking in, it's a very worrying sign. The type of sign that makes someone think "oh, hell, am I going to knock on the door one day and find a corpse where my friend used to be?"
It's even easier to understand Hisao's reluctance to leave, because Hanako is barely saying a word to him. She won't come out and just say "I appreciate the kindness, but I'm not going to hurt myself or anything. I just need some time alone for a few days, okay? Let me be, please."
There's a difference between communicating that you want alone time and shutting yourself in your room, not coming out for food, and not saying two words to the people you've been hanging out with every single day for weeks, if not months. One makes people think "I hope they feel better soon." The other? Well, look two paragraphs above...
If the circumstances in your life were similar, your friend probably assumed it was better to risk your friendship than to risk your life.
I don't know if that helps, but that's my take on the situation. I realize that Hisao's pressuring Hanako was overdone in that scene, but I always thought her outburst was too heavy-handed, as well. And maybe it works better that way - she was stressed, she wanted him to leave, he didn't, she felt threatened. Fair enough, it's understandable. We don't see the future, but I always imagined they'd reconcile, if not fully. With Lilly returning and being a mediator, they could've apologized to each other, but probably gotten over it. Mostly. Wouldn't be surprised if they were somewhat farther apart after that, but that's something time could overcome, eventually.
But if she stood by her angry words, and cut her friendship with Hisao forever? Well, that wouldn't be so understandable - she put up so many huge warning signs and refused to talk to anybody so much that there's no wonder people were worried about her. It's horribly alarming behavior. The fact that Hisao acted tactlessly in the bad ending doesn't change that. Suicide or self-harm are real things, and people will worry about that if you give them a reason to.
I honestly can't say whether it makes the same amount of sense in your real life scenario, since I don't know what it was like, but I have to play devil's advocate here. If your behavior underwent a strong change, if you refused to communicate with the people close to you ... people take those as warning signs. And it may make them act.
After Hanako's route, I understood the difference between caring and pitying: when you care about someone, you take into account his preferences and his needs, while when you pity someone, you just do what you think is best for him, but in reality, you do what is best for you to feel ok. That is something I have been throught for awhile, and it sucks. Fortunately, it was only one person who treated me like that. Unfortunately, it was my best friend.
If I could go back to when we were best friends with her knowing what I know today, I would confront her asking her directly if she was pitying me and hid things from me because she didn't want to hurt me. Instead of going throught the shit I did, it would give me an answer immediately. However, I am bold enough to confront other people that way, not you. I don;t know if you could do the same.
I still have trouble trying to tell the difference, really - but maybe that's because I can't make sense of "doing what is best for you to feel okay" in that situation. When I'd had friends who were in a bad emotional state, I went and did what seemed best for them, not what was best for me. There were things about the arrangements that I didn't like, but it wasn't about me. It seemed to help them, too. At the time.
I also have a very bad time with lying or concealing important facts. I do do it, at times, but usually, I say what seems to need to be said. Conversely, I don't say things that don't need to be - I'm rarely someone to be outright insulting, even to someone that has managed to earn my hatred, because what in the hell is that going to accomplish? I call people out on what they've done - major events they had a clear choice in - not random, insignificant flaws of their personality or body or whatever.
Maybe my issue there is that I'm not really capable of thinking "well, even if they don't like it, it's probably best for them". I don't think that outright antagonizing somebody is going to help anything. If they're reluctant to do something, find another way to persuade them to do it, or find an alternative - don't try to force them. I dunno.