How to unfriend someone without being harsh or get them to loath you

I know we all have that one friend we all wish we didn't have, but we love them but we just can't bare them. My friend ________ is that friend now and I know she is that friend because I get irritated by every little word she says. It took me months  to figure how to deliver the news and one day I HAD ENOUGH she had embarrassed me on fb by calling me a hypocrite and so I didn't speak to her for months and I just told her I think we aren't very compatible as friends anymore and that we should just go back to the days we just ignored each other we both sensed it. She understood entirely and I told her if sometime in the future we become more friendly toward each other then maybe we can go back to  friends or even best friends.