It might resonate the first time you hear it (most good propaganda does), but if you contemplate it for more than 10 seconds and you'll realize it's obviously untrue.
Also, you don't have to be macho or physically strong to be strong. That just seems like your own bias leaking into the discussion.
That it might promote contempt for weakness might be true, though, and it didn't cross my mind. I don't like that it does that. At the same time I don't think weakness should be glorified either. Ideally, weak people should be helped to develop their own strong self.
Bret Devereaux has a series of posts where he delves into the history of the idea behind the meme - https://acoup.blog/2020/01/17/collections-the-fremen-mirage-...
It's a thoroughly interesting debunking, and in part IIIb, he talks about how the trope was used to promote racial purity and superiority.
I don't know if it improves later, but they seem to only consider physical prowess as a form of strength. I generally interpreted this as strength of mind.
Also, I've taken the phrase less literally than they did. Man to me implied "human" (ie the same as man kind) because these quotes are usually designed to be succinct and memorable. They seem to think it's exclusive to human males.
But I've not read it in full yet, so we'll see when I finish it