how is that implied by 'a man likes to feel like a man'?

What's the context that you're imagining this topic coming up? Because from my perspective, as a man, if someone said this to me about someone else I'd assume that I'm being asked to come up with some made up work, so that some junior guy on my team, or some dude in my social group who is feeling down, can feel more useful.

Which I might or might not accommodate, but it's kinda patronizing and would effectively have the opposite effect in building up my respect for that man.