I'm not in my aero bars on my tt bike during a climb, but rather the bullhorns-- so breathing has 0 to do with it.
Not to start an argument with you, as we all know how unpleasant you can make that experience, but do you see something a little odd with the number of cyclists in this thread who seem to experience the SAME THING vs. the one individual who isn't agreeing?
Just sayin', maybe YOU should stop and think about it (or maybe find a hill to climb).