Antagonism means hostility. You might feel antagonism to the teacher who gave you a D on your last test, and she might be angry at you for not working harder––there's antagonism between you.
Antagonism is one of the few things you can share easily with someone you don't like. You might feel antagonism toward your school, or at least the idea of going to school. If you're an antagonistic person, you feel antagonism to lots of people and things.