Spoiler:
Quote Originally Posted by me
If you flip two coins and the FIRST is heads, the second being heads is 50/50. But if you flip two coins and EITHER one is heads the possibilities are:
The "trick" or whatever to the whole thing is that it's not that the first coin is heads but that either one of the coin is heads. We don't stop flipping when the first coin is tails, because only the second coin being heads still meets the requirement of "at least one of the coins/puppies is heads/male".

More succinctly: We don't know that the first coin is heads, we only know that one of either coins is heads, and therein lies the mindtrickery.