Did an American classmate tell you this? In my experience Americans often share their food. I know my children often share their lunches with their friends at school.

What you did was a very nice thing to do and perfectly natural.

I think it depends on how well you know the person. People here don't offer food to people they do not know. But in a class, I am thinking you see this teacher's helper every class session. I think you were very nice to offer your sandwich, and it isn't a strange thing at all! Perhaps your classmates are not very polite! If someone comes to visit in your home, it is polite to offer at least something to drink and also food, especially if it is around the time people eat a meal. But I think this depends on the culture and background of the family. My family background is Italian, and no one leaves an Italian home hungry. :)

Some do others don't. Most the time the reason people think this is because in most Asian cultures they sure food with all their guests. In America that's not necessarily the way we do things. I usually offer family that comes over food. Friends I offer drinks and sometimes food. Not very close friends I won't offer anything.