It would also lessen the intimacy of straight marriages if gay folks were allowed to get together. That would be sad. Because you know, your definition of what “intimacy” is should be the same as mine, and if mine differs then yours should override me. Because you’re not wrong, of course.
The argument above assumes that LGBT rights have only one leg to stand on: the right to absence of interference from the government. Since this is very much not true - otherwise marriage, partner benefits, health care decisions, and the like would cease to be points of contention - the entire argument is FAIL.