Nonsense. I started climbing mountains not long ago, and, having lifted weights for many years, was able to go further and faster than most experienced climbers. (Though of course in mountaineering your brain is more important than your legs.) Same with skiing, trail running, backpacking... strength helps with everything.

Your biceps and triceps must work against each other or you will have no control over what you're doing.

Sounds like you've fallen under the influence of quacks.