The answers here basically say, "because that's how the controls on a plane work."
There's still an obvious follow-up question: "why?"
Many planes have control yokes like this:
The yoke has two degrees of freedom: rotational and telescoping. It does not move horizontally or vertically. To pitch the plane up or down, you control the elevators by pulling or pushing the yoke towards or away from you, respectively. It's natural, in that if you lean your body forward, as if wanting to go down, then the nose points down.
Even in airplanes that are controlled by a stick…
… the convention remains the same: push down, pull up. Taken out of context, though, it would seem that the convention for the joystick is backwards.