From what I understand, it was primarily a political thing. The more groups that could be included, at least in theory, the broader the organization's base of support. My impression is that there are many gay & lesbian people who feel transgender people should not be included.
I don't know if I was actually transgender or not. I'm still confused about the whole thing. (For most of my life, the word didn't even exist.) And now it's just too late for it to make any difference. But I've never identified with the LGBT community. For me it was all perfectly simple... there were boys & there were girls. I was born a boy. But I always felt I should have been a girl.
I'm basically a pretty quiet, conservative person. And I've always been put off by the flamboyance that seems to characterize gay pride parades, etc. There was a trans YouTuber whose videos I used to follow. I don't believe she's uploading anymore. But in one of her videos (I still remember this) she said that she never wanted to stand out. She said she "simply wanted to be a woman in this world." For me, that was it in a nutshell.