Legendary Pokémon

I am fairly new to the Pokemon Universe.
Actually, I'm definately a noob.
I've only played X and Y.
When I'm on GTS I constantly see requests for Mew.
From what I have read so far on the Web, Mew can be obtained only through older Gen Titles and thet are not transferrable to X/Y.
So why, when I was trading with a Trainer was he able to tease me by showing off his Mew?
I would like to get a straight answer on this.
What Pokemon game can I get a Mew?
Is it a given I will get a Mew if I get the game?
Is Mew breedable?
Is transferrable to X/Y?
And if it is not, why do so many Trainers in GTS request it?

You can only get a Mew with an event so even if you buy previous generations' game you can't catch it.These Mew you see were transfered from previous generations.There was an event on HG/SS Gen IV which can be transfered to Gen V and then to Gen VI.There were probably events in Gen III which I didn't catch so there are Mew that can be transfered to X & Y.Mew is not breedable as most legendary pokemon.Also most of the mew that you see are were hacked in previous generations and transfered.

PS There is a pokemon related questions thread where you can post so you dont have to make a new thread everytime you want to ask something.