Nature exhibits its share of symmetry and mirroring. That's the thinking behind white holes, which are the theoretical opposite of black holes.
Black holes, of course, are those weird space objects with a gravitational pull so powerful that even light can't escape its grasp once it passes a point of no return called the event horizon. In theory, the event horizon of a white hole would do the opposite. Instead of pulling everything, it would push everything away.
Any matter near a white hole, in fact, would cause it to collapse. Because black holes do exist and form by the collapse of stars, matter is always present ... meaning that a white hole probably can't be a reality.
Black holes don't necessarily need an opposite. They may in fact just be a point in space that doesn't really have an "other" side. And for as weird as black holes are just by themselves, maybe that's a good thing.