Pokemon Breeding

Pokemon breed by combining their Aura, which through reasons unknown produces an Egg with an infant Pokemon inside. As stated in Pokemon X/Y, these Eggs are not truly eggs but instead more like "cradles" that contain the baby Pokemon who I presume is already fully developed. So when the Day Care Man says "We have no idea how it got there", he means "We really don't understand how two very different Pokemon can make another Pokemon with just Aura so please don't ask."
However, if two Pokemon are the same species (and opposite genders, of course) they're able to breed like any other creature, get pregnant, etc.
Finally, Pokemon don't consider mating as intimate or taboo as humans do. If their trainer/breeder wants them to mate, they will. It's just part of life to them and certainly isn't something to get all worked up over. So when Felix excitedly talks about mating his Pokemon, they'll only roll their eyes at how much he's freaking out over it.

Nicely worded! Thanks for posting this, and making the theory very clear and easy to follow.