That's kind of untrue.

We differentiate them as male and female because by definition females have larger less numerous sex cells than males, so by that definition the male has the babies.

But the male does basically everything, the eggs are fertilised in the male's body and it's the male who incubates them and keeps them at a stable temperature/safe from predators.
If we didn't use the relative size of sex cells and quantity as the reason to call one male and the other female we'd probably be identifying them the other way around because in almost every other species that's how it works; the male puts it's sex cells in the females body where it mixes with their sex cell and then the female looks after it until it's viable to be laid/born.

Kangaroo pouches are very different. They're for already partially developed baby kangaroos. The tiny baby kangaroo has to climb up the outside of the mother's body to reach the pouch.

TL;DR: Seahorse males are more like what we think a female reproductive system should be than a male reproductive system, a comparison to a kangaroos pouch is really inaccurate as a result.