Religious reason:
Mutah is allowed according to Quran (Open up Part 5 of 30 and see first page). And during the time of Prophet S.A.W.W it was practiced and then only during 2nd Caliphate it was prohibited (not by Prophet S.A.W.W himself).
Social and Common sense reason:
Mutah is allowed because Zina is not allowed at all. Nobody is forcing to do Mutah and it is for pious people who want themselves to be saved from even the slightest of the sins. So, with consent of the two (man and woman) it is done and is same like Nikah (Permanent) beside the two of them agrees to ending time. This is practiced to save yourself from sins. If people want to misuse anything, the same way they are bound not to misuse permanent marriage accord. Hope you get the point!