While both ideas seem aberrant to most Americans today they actually serve different social and practical purposes.
In fact male babies have a slightly higher mortality rate. War and hunting accidents also tend to leave a less than balanced gender population. If the ratio of women to men is lopsided, why not be sure that most men have a chance to reproduce? And if you are church looking for people to tithe or a government looking for soldiers to throw at an enemy, why not produce as many babies as possible?
Another reason to have multiple wives is strictly political. Alliances can be formed by marriages. Clan feuds, tribal rifts and national wars have been smoothed over by allying the combatants in marriage. Even non-kings can make alliances this way. The British diplomat and warrior, T.E. Lawrence (aka Lawrence of Arabia) ended up with almost 50 wives in the course of his paving the way for the British and British Petroleum in the Middle East.
Of course in cultures where this is common the most powerful men often have so many wives that they don’t actually have sex but a few of them. A huge harem of wives and concubines hasn’t always been a playboy paradise. It has been a world of intrigue, murder, jockeying for position of the various children from favored wives or lovers. Like so many areas where excess does not lead to happiness, having dozens or even hundreds of wives can be more of a difficulty than pleasure palace.
If polygyny is about producing more, polyandry is a response to scarcity. If your land is hard to farm and does not produce ample fodder for large herds it does not behoove you to be having a lot of children. No matter how many husbands a woman has, she is unlikely to produce more than a child every year or two. So in places with very limited resources it is not uncommon for a woman to marry the eldest brother in a family and be considered married to all of his younger male siblings. Often the younger brothers travel with the heard, or take jobs in the city to support the family. Usually the eldest inherits the herd or the land and is expected to use it to keep all of the siblings alive and well.
This is found in high mountainous regions like Tibet, areas of India and Nepal as well as some islands on the South Pacific. Few societies thrive in environments inhospitable enough to make polyandry as common as polygyny. But both arrangements solve societal problems and help a community deal with different problems.