Dollars to donuts, this is the reason. Access to flight at 7th level is perfectly reasonable - Wizards can learn the fly spell by then. However, they don’t want you having a Large companion that early, and they’re probably worried that a Medium sized creature flying on a Medium sized mount would strain suspension of disbelief. So, Medium characters get to ride it at 7th but can’t fly on it until 15th. And since they don’t want Small characters to make objectively better Drakewardens than Medium ones, neither can Small characters.
Not saying it’s a good decision, but I’m positive that’s the logic behind it.