For the very simple reason that if ANYTHING is big enough, its own gravity will pull it into this shape. Everything gets pulled towards the middle, and the shape where everything is closest to the middle is a sphere.
This is part of the definition of a planet. There are three conditions that make something a planet and one of those is that it is in hydrostatic equilibrium. Which means that it is big enough for this to have happened. Maybe it's not exactly spherical because it's spinning, so it will bulge in the middle, so that's why we say "in hydrostatic equilibrium" instead of "spherical".
If an object is too small to have achieved this, like an asteroid or a comet, then it won't be smoothly rounded like a planet.