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Perhaps a better way of looking at it might be that we don't understand why electromagnetic effects don't dominate over large scales but gravity does. To me at least it seems like there's something odd that the weakest of the fundamental forces (if it is a force) controls the way things move throughout the universe while, to the best of my knowledge, the effects of the electroweak force and the strong nuclear force are not observed over galactic scales.
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Gravity dominates because it only has one sign. All matter (and anti-matter, for that matter #-o
ops: ) has positive mass. So, gravity is cumulative. The electromagnetic field of an object can be positive, negative or neutral. If you have a positively charged and a negatively charged body in proximity, they will be strongly attracted to each other. However, at a distance from the two, they cancel out and have no effect.
Gravity and the electromagnetic force have infinite range because their respective bosons have zero rest mass. The strong and weak nuclear forces are carried by (relatively) massive bosons, so they are limited in range to the confines of the nucleus.