but the line is a fine and debatable one.
I think the line is not "fine" it is wide, very wide. There were many species (but we have only a few) that were "in the line". Those that we have to argue over which side they are on.
That is the whole point. Today we have only birds and not-birds. That is the result of the ongoing branching and pruning of living things. Archy is neither; if you take defining characteristics of birds but ONLY stick to what we need to separate them TODAY then archy is, (I think -- not a taxonimist) a bird. However, when we want to separate archy from dinos then we run into the wide grey fuzzy line.