Because it's entirely dependent on sampling assumptions. Go to a random house where there's two children, one of which randomly opens the door. Each bb, gg, bg, gb is equal probability and a random child opens the door.

Now if you see a boy disregard that since you can't make the statement that one is a girl.

If you see a girl go ahead and make the statement "a family has two children. You're told that at least one of them is a girl.

What is the probability now?

You have twice the chance of making that statement if you encounter a gg family over a bg/gb family right since there's one of two girls possibly answering the door amongst those families.

So 50% chance of that statement being enabled from a gg family, 25% chance coming from a bg family, 25% chance of coming from a gb family. Which means 50% chance the other child's a girl and 50% chance the other childs a boy.

The probabilities here are entirely dependent on details of the sampling which is not made explicit here.

Paradoxes don't exist in reality (they do in hypothetical situations), so there is indeed no paradox as you correctly observe. Instead, most people answer this wrongly, for some reason. And for some reason we call situations where this happens "a paradox". Though I agree that we shouldn't.

Edit, ok, there are things like "This statement is false.", but we should perhaps stick to "self-referential problems" with those.

I think paradoxes just exist in our theories, languages, and formal systems when we make flawed assumptions or create inconsistent frameworks. But physical reality itself just is what it is - no contradictions, just phenomena we sometimes struggle to describe accurately.

If contradictions (paradoxes) can exist, then anything becomes possible through the principle of "explosion in logic". From a contradiction, any statement can be "proven" true. The whole foundation of rational thought would be undermined. Right?

The “paradox” may become apparent if you think the answer to all the questions below is the same (2/3). And if it’s not the same, why not?

——

You meet three people:

Alice has two children. You're told that at least one of them is a girl.

Bob has two children. You're told that at least one of them is a boy.

Csilla has two children. You're told that at least one of them is a lány. That clearly meant boy or girl because of the context, but you don’t know enough Hungarian to know what it is.

For each of them, what's the probability that they have a girl and a boy?

—-

You meet all the parents with two children in your neighborhood. Say there are 60 such families.

For 30 of them you’re told that at least one of them is a boy. What's the probability that they have a girl and a boy?

For the other 30 you’re told that at least one of them is a girl. What's the probability that they have a girl and a boy?

Confusing permutations and combinations