The question is asked as though the person asking assumes that actual monogamy is a requirement for marriage. It isn’t in most places, even though current marriage laws will only allow monogamy in the legal sense.
For the purpose of this question and answer, I will include any form of honest nonmonogamy, or any label applied, such as open relationship, open marriage, swinging, swapping, polyamory, polyfidelity and polygamy.
Why do swingers get married?
Why do people in open relationships get married?
Why do polyamorous people get married?
The short answer is: For the same reason most other people get married. They want to get married, they think it is the best thing to do at that time in life, or they’re pressured.
There are many reasons to get married, and as I noted, one doesn’t actually need to be monogamous to get married, unless one wants to be ethical and married to someone who needs and demands monogamy. People get married for love, for attraction, for companionship, to solemnize or make official their relationship, for religious reasons, to make a public statement, for sex, for children, for friendship, for benefits, for insurance, to pool resources, to co-parent, for career, for money, as a form of commitment, to apply a legal structure to their relationship, and for other reasons I’m probably forgetting. Nonmonogamists who marry do so for one or more of these reasons, just like anyone else.
Some people cite the marriage vow of "forsaking all others." But that is just ONE vow, not one that all people marrying make. The vow can also mean different things to different marriages.
Some nonmonogamists decline to marry for various reasons. Some, like some monogamists, have decided to decline until everyone can get married. Some decline to marry until everyone in their polycule can marry. Some can’t have a legal marriage for their polycule until there is full marriage equality.
The question can also be asked of monogamists: Why do you get married? Not only is actual monogamy not a requirement, in many places, of our restrictive marriage laws, but one can be monogamous without being married.