I'm going to stop paying attention in the middle of a conversation with someone.
Why are you not going to listen to them?
They are boring and what they have to say is boring.
I understand that what the other person has to say to you may not pique your interest, but not listening to them is rude and inconsiderate. Finish your conversation and hear what they have to say.
It's not a big deal, just a little bit of rudeness. People should learn to deal with rudeness.
Just because other people are rude, that doesn't justify your rude behavior. You should do your best to be present in conversations you're part of. And you might find it interesting if  you take the time to pay attention!