While technically I guess someone who’s bisexual could be described as “both straight and gay”, I also understand that, in spite of its inclusiveness, such a description could be seen as relegating a bisexual person to the very categories they’re trying to break out of.
There’s also have the idea of a “gay community”, so I understand some people who are bisexual wanting to carve out a community of their own, or at least have a subgroup that’s part of the LGBT community while emphasizing their distinctiveness.