"Baby dragon" is a very ambiguous term. We don't know much about MLP dragons, so that term could be used to refer to young dragons that haven't reached certain maturity. As ambiguous as this is, one may argue that "baby dragon" is a term used for those under the age of 10, 20, etc. Because we simply do not know about this. The very same way you say that Twilight was a filly of unspecified age, can apply to a dragon.
How old can a filly be before being considered a teen/young mare? I don't blame you for saying that Spike, may in fact, be under the age 10. But using that logic, you're contradicting yourself.
At the end of the day, neither of us is wrong, because we simply do not know how age terms work in Equestria unless I find that tweet