Why even be offended by such a small thing? What's even the point of greeting though? I can see it makes sense when you want to talk to someone. The "hey", "hello" or whatever can work to grab attention and they can acknowledge that by responding back as opposed to immediately talking and the other person missing part of or the entire first sentence, if not more.

But otherwise, there's a good chance it's distracting or even distressing.

I usually try to greet back unless it's awkwardly late because I didn't expect it, as such it caught me off guard and I was thinking what I am supposed to do and what they want from me for too long.
But this generally makes me forget what I was just thinking of or what I was doing and makes me anxious. Then I may even be thinking of how I handled that for the next few minutes. I hate that.

Don't get me wrong, I am not mad people for greeting me, I know they just do that, but I'd rather not them do it. And as such I won't greet anyone either unless I need to talk to them. I don't want to cause same issues to others only to say "Hi".

they looked at me, said nothing, kept talking to themselves.

Yep. Sounds familiar. "Am I supposed to say something? I am paying attention, I am looking at you. Go on. Oh, nothing, OK..."