By nature, humans have three main objectives, survive until you can mate, mate, have children that reproduce. The more mates a human has, the more children there are to survive to reproduce, and so on and so forth. Polygamy achieves all three basic goals, you've just had children, so you have survived to reproduce, and having more children makes it more likely one of them can reproduce themselves.
Yes, there are affairs, divorces etc, but that is more to do with personality than an affliction of nature. Of course men and women look for alternatives when they are unhappy in their relationship- the key is not so much that humans are polygamous - it is more to do with the fact they look for other men and women when they are unhappy with their respective sex lives.