I hate when random people say hi
What's wrong with them saying hi?
It makes me feel like I'm some kind of a public property.
I think these people are just trying to be nice to you by saying hi. I don't think you shouldn't take it so personally.
I feel like stabbing them in the face.
You need to learn to manage your anger. You shouldn't be so angry over something as small as this. If you don't wanna greet people back it's fine, just ignore them even if it's not a nice thing to do.