I want to skip this birthday celebration with my friends because they changed plans on me.
Don't you want to celebrate with your friends?
No. I hate having birthday events.
You should go to the birthday celebration. Your friends are looking to have a good time and invited you so you should at least make an appearance. Even if you don't stay the whole time, you should show up so they know you care.
I don't think they care about me so I'm not going to care about them.
It sounds to me like they care about you if they invited you to a birthday party. People don't usually invite people to a party if they don't like that person. This may just all be a misunderstanding that can be worked out if you talk to them about how you are feeling.