The reason people don't like the term "polygamy" is because it it illegal in the U.S., Canada and a whole bunch of other countries in the world.
In Canada, for example, it's part of the Criminal Code of Canada - Under s 293(a), everyone who enters into any form of polygamy or any "conjugal union with more than one person at a time" is guilty of an offense, and under s293(b), there is a separate offense for any person who "celebrates, assists or is a party to a rite that sanctions a polygamous marriage".
Now, whether the law is enforced in situations that are fully consensual (which include not underage) is a matter of question, of course.
Polygamy means "married to many" and it is that part that is illegal. Polyamory - "in love with many" is not illegal.
So while there are efforts to decriminalize it, it's a little more than some Mormon-related stigma attached to the term. Some people don't want to adopt a term to describe their relationships which are singled-out in the legal system as a crime. I can understand that concern...
For those curious, here is the exact text of the Canadian law:
- 293. (1) Every one who
is guilty of an indictable offence and liable to imprisonment for a term not exceeding five years.
- (a) practises or enters into or in any manner agrees or consents to practise or enter into
whether or not it is by law recognized as a binding form of marriage, or
- (i) any form of polygamy, or
- (ii) any kind of conjugal union with more than one person at the same time,
- (b) celebrates, assists or is a party to a rite, ceremony, contract or consent that purports to sanction a relationship mentioned in subparagraph (a)(i) or (ii),
(2) Where an accused is charged with an offence under this section, no averment or proof of the method by which the alleged relationship was entered into, agreed to or consented to is necessary in the indictment or on the trial of the accused, nor is it necessary on the trial to prove that the persons who are alleged to have entered into the relationship had or intended to have sexual intercourse.