Birds are descended from dinosaurs, that much is pretty clear, even to a layman like me. I can hardly look at a pigeon walking around on a street without seeing the theropod resemblance. I'm completely willing to accept that at some point (late Triassic, Wikipedia tells me), the most early things we can think of as birds (perhaps archaeopteryx) branched off from other bird-like theropods. What confuses me is when a scientist claims that we should actually classify birds as modern dinosaurs, that is, their class would surely be reptilia rather than aves, and their order surely that of the dinosaurs (though there doesn't seem to be an agreed order). This system of classification frustrates the neat-freak in me. It seems that, under these rules, any species is included in its ancestral groups as well as its own. In that case, why am I not, alongside being a hominid, an ape, a primate, and a mammal, also reptile, an amphibian, a fish, a polyp, a protozoan? I was taught biology such that all species could be given eight taxonomic specifications, and as I understood it, a new class, such as mammals, could pop out of a single species; the very last of the reptilian mammals before we draw the line between reptiles and mammals. This system makes way for future classifications. The system proposed by the idea that birds should be considered dinosaurs will lead to the long-term piling up of taxa, or an infinite line of new sub-special groups being made up for the sake of new classifications.
But of course, as I understand it, the birds = dinosaurs thing is put in place due to birds being more closely related to dinosaurs. But I'm still not sure what this means. When is a thing more closely related to another thing? When it branches of later in time? When there is less morphological difference than otherwise? Someone please help.