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The use of "they" as a preferred pronoun for individuals sometimes happens when people want to identify as nonbinary. I've also seen trans people list gendered and gender neutral pronouns together--for example, saying my preferred pronouns are she/them.
I think it's mostly political. Some believe that gender neutral language decreases sexism. Others, having absorbed these theoretical/political perspectives as truth, sincerely view themselves as nonbinary. They view others' refusal to use they/them pronouns as an attack on their immutable selves.
What's interesting is that we could have a tolerant society that allows men and women to express themselves however they like, where women can be masculine, and men can be feminine. In this case, we recognize that the sexes exist but don't force behaviors on people on the basis of their sex. This approach is consistent with liberalism. We're all free to express ourselves and make our own decisions. Nobody is allowed to infringe on that freedom, but we're also not allowed to impose our ideas about self expression on others.
Instead, we see the current trans movement arguing that everybody has an immutable gender identity with infinite values along a spectrum from male to female, then asserting that this subjective identity ought to be recognized as such by all other people and the government. This cannot work in a free and liberal society. We cannot have a functioning pluralistic society in which everybody has to acknowledge and affirm the subjectivity of each and every other person. First, it's totalitarian to force others to accept our subjectivities as truthful. Second, it's narcissistic and antisocial. We have to agee to some shared structures of meaning in order to live among and communicate with others.