RH, the taxonomic system may be somewhat arbitrary but only somewhat. That birds should be ranked with reptiles on the basis of flight, however, is well, let's say, just not copasetic. Birds have some dinosaurian ancestors to be sure, but they are quite distinct from reptiles now. And if flight were your criteria, Mammals and all manner of other things would be in there as well.
The levels of classification follow a general concept of phylogenetic relatedness. Everyone in a particular category (class, genus, whatever) should have a common ancestry that is distinctly different than everyone else in the other categories at that same level. In that way, birds are a pretty good monophyletic group relative to reptiles (or mammals for that matter). That there are errors in the taxonomy is no secret, but like all errors they are corrected when ferreted out. That said, there are no birds mistakenly lost in the reptilian part of the evolutionary tree or vise versa.
