I'm just copy & pasting Wikipedia;

Dinosaurs (including birds) are members of the natural group Reptilia. Their biology does not precisely correspond to the antiquated class Reptilia of Linnaean taxonomy, consisting of cold-blooded amniotes without fur or feathers. As Linnean taxonomy was formulated for modern animals prior to the study of evolution and paleontology, it fails to account for extinct animals with intermediate traits between traditional classes.

But reptiles is more a culturally based category than a strictly defined biological class, so you might prefer a definition that excludes dinosaurs, and that's fine. I'll admit, it seems odd to class birds as reptiles, and strictly speaking if you exclude birds you should exclude dinos too.