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It is possible to love more than one person at a time.
People who love more than one person deserve the same level of recognition under the law as do people who love only one person.
The definition of marriage as between two people stigmatizes all forms of open or polyamorous relationship.
If all parties concerned consent on it, it does not harm any external parties.
The definition of marriage as between two people legitimizes monogamy as the one true way to love.
it isn't necessarily wrong. We might not follow it, but if the people in the party are okay with it, why does it matter?
In many countries, marriage is only a contract between 2 people with a set of legal rules only valid with 2 people.
A mariage with 3 people is no more possible than than playing tennis with 3 players.
We first need to make a new set of rules. And it may be extremely complicated.
The government should not have the authority to issue marriage licenses.
Polygamy has been one of the greatest oppressors of women in all of history, particularly when administered by fundamentalists religions. Pedophilia, selling child brides, and abuse are highly linked to polygamy. It's bad for men too, since only the wealthy have access to marriage.
Marriage exists so that societies may have cohesive families in order to generate progeny. Allowing multiple partners within such a family would serve to increase progeny. Thus, it serves the societal purpose of marriage even better than monogamy.
if polygamy is legal, polyandry should be legalized too
Polygamy leads to certain partners being favoured over others, possibly causing conflicts between the parties and/or depression.
It's in our DNA, kind of. Read source. TL;DR We are "monogam-ish" depending on social status.
This would leave some people dissatisfied and without partner. If there were 10 people (5m/5w) on earth and 1 woman married 3 men, 4 women must fight over 2 men. This may only work if receiving/giving polygamist parties are balanced in numbers.