Locker room version: men will say nipple without any issue when talking about the nipple itself, or chest or pecks if talking about the fleshy bits behind said nipple. If someone is a bit overweight they might call them man-boobs, moobs, or similar. Usually it's gentle ribbing rather than intended offense, but sometimes it is intended to be a bit cruel depending on the tone. I have never heard a man refer to their "breast" in any context.
If you ask a man if they have breasts, you will get 99% "no" as the answer. You can't refer to a body part you don't have.
I might be in a bubble though. Hope this helps.