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Maester
The most common version of this seems to be "masculinity isn't about physical strength, it's about standing up for what you believe in." Gravity Falls did this one straight in the episode where Dipper meets the Manotaurs--they provide a ludicrously exaggerated model of conventional manliness ("I have six Y chromosomes, three Adam's apples, pecs on my abs, and fists for nipples!"), and he provides an alternative model by recognizing them as bullies and standing up to them. Dexter's Laboratory, on the other hand, goes straight for the parody ("It's not the beard on the outside that counts; it's the beard on the inside!")
I must not remember that episode of Dexter's Laboratory. I'd thought I'd seen them all. *off to Youtube*
Yeah, I've seen more parody attempts than realistic examination of societal expectations of manliness, and while parody does have its place...it doesn't really offer up any viable alternatives.
I'm not saying I have the answer here, on what non-traditional manliness is like or how it should be portrayed, but I don't think that the current expectations put on men are the way to go. (For one thing, they lead to the creepy, stalker idea of romance.)