They just want the (other person's) feelings to go away.

While it may seem that this is the case with conflict/intimacy
avoiders in many ways this is just a result of a fear of their
own emotions . Even more than anothers emotions their
own strong feelings are trying to be negated, they are
afraid of their own feelings. I used to be like this avoiding
conflict because I did not know how to deal with the anger that
would arise inside of myself.