There is no logical reason. It makes no sense in-universe. There was no explanation given in-universe. Just like a lot of things. So instead we will proceed to develop illogical reasons in this thread.
500 years ago, some guy named Alan the Barbarian of China (ABC) wanted to enslave a bunch of black people in order to build an ice cream factory for his kids. So he went to Africa to capture the black people, but all he found were a bunch of animals. These Pokemon were the ancestors (not-so-ancient ancestors to be exact) of all the Pokemon that now evolve through trading. Thinking "what the hell" he took them and proceeded to use them. Now, Captain Native America did not take too kindly to this, and his native sense triggered. Yes, from halfway across the world.
So he flew through the center of the Earth to confront Mr. ABC. After they fought each other in Mortal Kombat, ABC turned into a giant dragon, which was promptly killed by the armies of the Buddah. The Pokemon having been freed, this brought on such a sense of euphoria that it proceeded to cause them to evolve on the spot. As for those who only hold items when they evolve, well, they were so used to working with certain flavors (ABC made many flavors) that it became a tradition of sorts to destroy the things that went into them or use them as weapons. Hence, why the items disappear after trading (because they infuse with them).
Several hundred years later, a device to do this manually was created, but because there had to be motion for it to work and they also had to go from one person to another it was built into trade machines.
See? Not so hard. Just think of stuff and type it as it comes to mind. Then we'll have a bunch of explanations in lieu of an official one or one "that makes sense" (really, 9/10 fan theories suck, so we may as well go all out for the hell of it).
EDIT: Because GrnMarvl13 doesn't like me, I'll clarify that the whole "taken from a bad trainer and evolved due to euphoria then it became tradition to evolve when changing hands whether it was from a bad trainer or not" thing does indeed make some sense. If we assume something like that happened. Even in silliness, there's backing. I still think many fan theories are stupid, though. Including this one.