Ever wondered why Mew is so hard to catch? Well, Mew is always hidden around. She never wants you to find her. By now, you've either; already found out why, or will learn why in a minute.

Mew's Baby

Something just isn't right about Mew. She's almost impossible to find; let alone catch. Why could this be? Possibly, she doesn't want you to catch her. But I have a better theory. My reason is given in the fact, that Mew had a child. I even have proof from the game. Here's a photo, to the right, and here's my theory.
Mew's Child.

Diary from the Pokemon Blue/Red Games.

So, Mew once had a child, right? Well this would obviously be a reason she was hidden. Another, is that her child was the one who was found, instead of Mew. They killed her child, in order to create Mewtwo out of her DNA. This makes sense, considering Mew loves children. As seen in the first Pokémon Movie. Mew saves Ash from smashing on the statue and dying. Then, she plays around with him. But when she sees Mewtwo, she loses her "happy" attitude, and starts to attack Mewtwo ferociously. 

Since Mew's Child was killed, she was put into great depression, and hides. This also keeps her safe from being tested on, and made into "Mewthree"  

Final Words

I thought about this for a little bit, and thought it definitaly made sence. Mew had a child, and it's DNA was made into Mewtwo. That's why she hates Mewtwo, as her child was a sacrafice to make him. I don't know, I thought this was a good theory, and this explains why Mew is still alive. Please leave me some feedback in the comments. Thank you. -PastaIsCreepy