The motives aren't always violence, though. Add alcohol or some other drug to a wild party, and someone will eventually end up a part of someone else's good time, willingly or no. In these cases, the violators are too distracted by mating drive and the effects of whatever substance they're abusing to understand the consequences of their actions, and the victims may be too trashed to put up enough complaint to stop it. Other such scenarios are in plenty. Some just don't understand how this act affects a person psychologically.
However, there are plenty of cases of rape that have truly violent intentions behind them, and I think that the only way to understand why a person would commit such an act would be to work out how and why you would do so. Measure out chains of events and decisions that would realistically lead you to commit this sort of crime. Perhaps there are even circumstances under which you could fool yourself into thinking it's justified.
As for humans being the only animal that has sex for pleasure, not so. All animals find sex pleasurable. This includes dolphins, who also share with us the ability and likelihood of commiting the act of rape. Other animals just don't make as much an issue of it as humans; they were never really taught to feel especially violated over it, and they were never taught that it was wrong. It remains, however, that it occurs.