This is a really really valid point. This is a HUGE problem, believe me.
In fact, here's what happened to me - I got notified in my feed that a friend of mine kept liking her ex-boyfriend's music page, and I got this continuously, consistently for several weeks in my feed. After a while, I got pissed off, sent her a long E-mail , advising her to forget the past and move on. At that time, I didn't know Facebook was the culprit. She naturally was shocked+agitated and defended herself after which I thought she was lying and deleted her from my list. Today, we both are no longer friends. All thanks to Facebook. So, atleast in my case, it did more harm than good.
If you stopped being friends (I assume you mean real friends, not FB friends) with someone because of a single FB like you couldn't have been very good friends to begin with.
No you didn't get it, I stopped being her friend not because of the like, but because I thought she was lying, as I had data that spoke exactly the opposite of what she said.