I wouldn't be so quick to say it's an alt-right joke. Plenty of my friends will describe something/someone as a Chad and it has nothing to do with incel/alt-right cultures. Are those kind of phrases thrown out in those circles? Yes, but that's more of the general meme/internet lingo as opposed to subscribing to an ideology.
No, it really didn’t. Even if it did, it has since transcended into something more general that many people are familiar with. Ending your statement with “be better” is condescending and seems purposefully antagonistic. How about you lead by example?