How to describe someone who doesn't listen well

Depending on the exact reason for the listener doing this, you might say that he is impulsive, if he is interrupting because it is the first thing that comes into his head, or that he is impatient, because he can't wait to put his ha'pence worth in, or he might be intolerant, if he wants to suppress or pre-empt any possibility of a dissenting (or concurring) opinion.

I would call them bad listener.

Without assigning motivation to the act as @Brian Hooper's options do, I'd suggest boorish, uncouth, or simply rude.