Actually, there is a way for this to happen.
New game mechanics for Pokémon X and Y allow for either parent to pass on egg moves! So if you have a male Squirtle with Water Spout and a female Squirtle with Aqua Ring, you can breed for a Squirtle with both moves.
So to get a Squirtle with Water Spout, the best method is to catch a male Wailmer, level it up to 34, and then breed with a female Remoraid to get a Remoraid with Water Spout. Then you have to get a female Squirtle (or anything in its evolution line - this may take a while as 87.5% are Male) and breed the two to get a Squirtle with Water Spout.
To get a Squirtle with Aqua Ring, the easiest way I've found is to get a Marill, level it up to 28, and then breed with a female Squirtle/Wartortle/Blastoise.
Make sure one of the two Squirtles you breeded is female, and then breed the two together to get a Squirtle with both moves.
So it's a lot of work, but the point is that you can do it (provided that your game is Gen VI or later). Hope I helped!
Source (proof that egg moves can now be passed on by parents of either gender)