Back in the early aughts, I was hanging out one night with a mixed group that included some LGBTQ people. One complained about this sentiment exactly, with utter incomprehension how anyone could feel that way. I did have some formless idea how a bigoted person could genuinely feel this way, even though it had an inhumane effect. I struggled to express what I was thinking, but since I didn't understand what I understood, so to speak, I was not very successful.
People took me at my word, and we were all mystified together.
I continued to think about this issue for years, until I had acquired a sufficient understanding of the human experience to express my instinctual thoughts clearly.
It's about identity, as so much in discrimination and hate is. Identity is the construct that goes to the most intimate and fundamental understanding you have of you, and everyone has about themselves. These bigoted, married people identified part of their value and accomplishment, part of their status as people as husbands and wives. They imbued their own identity with the tremendous accord afforded to the institution of marriage by federal, state, and local governments, as well as their church and the society at large
They tied their identity to this institution, which was to all appearances one of the most stable and unchanging in meaning and status. The whole structure of respectable society depends on the operation of this institution; it's an attractive peg to hang your identity on.
When LGBTQ people were given access to this institution, it did change the meaning of it. It was narrowly defined, and was broadened. That change seems to cause no harm to us progressive folks, but those who had remade their own image of themselves to embrace the status of this institution felt their threatened by their own identity changing.
They objected in this seeming nonsensical way because they didn't see their own marriage as distinct from the impersonal institution of marriage. They identified with the institution, because of the way that magnified their own value and status as people.