And us mammals are furry reptiles by the same reasoning. ;P
Anyway, as far as I'm concerned, a group of warm-blooded, pillar-legged, often feathery or bristly (potentially everything below a certain size/exterior temperature), highly active animals which gain more energy from breathing than chemical reaction, have skeletal air sacs, and in some cases wings, semi-bird-like brain structures and extensive childrearing behaviour, can't broadly be described as 'reptile'. Even the earliest dinosaurs have a sizeable number of non-reptile traits; the best you can say is that aspects of them are reptilian.
Oh dear. Pedantry levels reaching critical status. It's gonna blow, cap'n.
Anyway, you're in good company Doom. David Attenborough continually refers to dinosaurs as reptiles, and the Mesozoic as the 'age of reptiles', to the continual grinding of my teeth. And it's not wrong, 'reptile' isn't a phyletic term, it just grinds my gears. Takes me back to a time when scientists thought dinosaurs were lumbering incompetents destined for obsolescence and extinction. Don't tell any herpetologists I said that, though.