I was friends with a colleague for a couple of years. We got into a disagreement. We were both upset. She felt she was being blamed and wound up telling me I had a mental problem. I was extremely offended and more hurt still that she refused to apologize. She says I am giving her ultimatums and still stands by what she says and still refuses to apologize yet she doesn't seem to understand why, given that, I don't want to be friends anymore.

You can't let it go and she won't take back what she said because she thinks it's true.

Sounds to me like there wasn't much of a friendship to begin with. Not much of a loss.

Not my personal phylosophy but I was told this saying a long time ago:

"Never apologize....

Your friends don't need it and .....your enemies wouldn't believe you anyway...."

You can be civil without being friends. I highly recommend that course of action. Roommates, neighbors, club members, etc.; those that have some commonality in their interests can be friends. Colleagues normally don't have enough to share.

What was the disagreement about? Did you stick to the topic or did you insult her as well?