When I think of boy bands, I think of bands who don't play their own instruments, usually don't write their own songs, and are very young. Their songs are fun, upbeat pop songs with no substance to them. Their music doesn't transcend generations, like the Eagles' music has. (There's several of us here who weren't born when the Eagles broke up or when they reunited, myself included.) A boy band's target audience is preteen girls. The Eagles audience consists of both sexes and there is no age limit or requirement.
No, the Eagles aren't a boy band.