dnd 5th – Does a PC have a CR (relative to the polymorphic spell)

Was he discussing the fate with my DM in connection with this discussion (Can an assistant PC polymorphize low-level animals into overpowering animals?) About the polymorphic spell.

According to Polymorph's description,

The new form can be any beast whose challenge score is equal to or equal to
below the target (or at the target level, if it does not have
challenge assessment).

I was excited by the idea of ‚Äč‚Äčturning one of my group members into a giant monkey or t-rex, but my DM said that anyway, with our current level (lvl 9), I would only be able to turn it into a monster CR 4.
He bases his judgment on this part:

The new form can be any beast whose challenge score is equal to or equal to
less than the target

From my understanding, PCs do not have CRs because CRs seem to have been invented to adapt monster levels to player levels (DD3). In other cases, we could simply assign experience levels to the monsters instead of creating an alternative ranking system. And why does the spell specify:

(or the level of the target if it does not have a challenge rating).

But I'm still relatively new to the DD5 world, so maybe I'm wrong. I understand anyway that the DM is the rule at the end of the day and that I have no problem. But I was wondering if there were points of precision in the rules that I could show him if it was only a problem of interpretation.