I wouldn't say that it's literally impossible, but consider that whales and dolphins are also mammals and they still breathe air despite spending their entire lives in water.

How are you going to find humans that can extract oxygen from water in the first place?

Selective breeding requires stock that has at least a related trait to the desired outcome. Humans don't.

You could breed for longer breath holding, etc, but unless you got lucky with a mutation, you can't magically produce a trait that isn't available.

Now, you could definitely start diddling genes in one way or another and get there with some luck and good protocols but that's not selective breeding.

At some point, you would run into a wall that requires evolution or other genetic changes to happen, and that ends selective breeding entirely. You could then start the breeding program again, but I say that isn't the same thing.

Probably not. Mammals and birds demand 10~100 times more oxygen to survive than other vertebrates (source), as our metabolism is rather high; I don't think that the oxygen in water is able to supply that. And a change in that metabolic rate seems a bit too involved to be feasible, specially given that our brains use a lot of energy (thus oxygen).

I doubt it, but I have read about a tribe that selectively bred themselves to be able to hold their breath for an unreasonably long amount of time.

edit: Added a word without which the sentence doesn't make sense.

I almost want to say you'd have better luck breeding super intelligent fish

So reading this question sent me into a shallow-dive (one article deep) reading about animals that have this capability seems to suggest that actually selective breeding (as opposed to natural selection) might be the only way to create a species that could breathe both on land and underwater, as it seems like otherwise the tradeoff of creating two seperate breathing systems just wouldnt be worth the cost in the wild.

btw not a biologist, so everything i write is probably BS

Not through selective breeding. Maybe through gene manipulation, but I don't think the science is quite there yet for something as dramatic as that. You could for a tail, since we used to have tails and sometimes people still grow a small one.

no idea, but thanks for spelling "breathe" correctly.

Maybe, if you already have a human with the genetic capacity to do so.

Yes. You will need trillions of dollars and operate outside of any country so you're not subject to pesky ethics and humanitarian laws. Good luck, I hope I never see you.