I'm not going to attend my friends new year party because someone who I do not like is going.
If you can just ignore the person and attend the party it will show your friend that you respect them and that you are mature enough to take the high road.
I just do not want to have anything to do with him.
If you have a legit reason to avoid this person than your friend will understand, but if you believe that you could attend the event anyway it will show your friend that you respect them, so consider how they feel before you decide not to go.
They'll be asking me why did I not attend their party. I can't avoid the issue.
You don't have to avoid any issue. Just tell them the reason why. Your friends will understand.