Offended

Just curious, im not a politically correct person by any means. But anything that depicts minorities in a negative light offends me. Today I got in an argument with a woman online because she posted something that I found offensive about the LBGTQ community. I just simply commented that I found it offensive because of its implication. This really upset her. She went on and on about how horrible it was to find something offensive. I kept asking "why do you care what offends me?" And she wouldn't answer.
Why do some people care so much about what others think or feel? Me being offended by something has no effect on you. It effects me and my life only. I find something offensive and then I move on with my day. I don't ask people to mold their opinions or actions to my beliefs. So why do people act like my being offended about racist, antisemitic or anti LGBTQ rhetoric is SO horrible? If you did something that offended me, and you don't care, move on with your life. I've moved on with mine. Stop trying to tell people what to think and feel. Some people are more sensitive than others. Why do you all care so much? If it's your free speech to be racist, it's my free speech to say I'm offended by your racism.