Polymorph can't turn creatures into dragons, only beasts
The polymorph spell's description says "new form" at first, but then later specifies that the new form must be a beast (emphasis mine):
This spell transforms a creature with at least 1 hit point that you can see within range into a new form. [...] The new form can be any beast whose challenge rating is equal to or less than the target's (or the target's level, if it doesn't have a challenge rating).
When the game says "beast", it is talking about a specifically defined game term. Every creature in D&D 5e has a type, and beast is one of those types. You can find a creature's type at the top of its statblock, just under the creature name, listed after its size (e.g. "Medium beast").
If the statblock for a creature says "beast" as its type, then it is applicable for the polymorph spell to turn a creature into that form. Anything else (dragon, fiend, aberration, fey, etc.) is not allowed.
A dragon is not a beast
If you look at an adult red dragon's statblock, it says: "dragon". Since it does not say "beast", it is not an applicable form for polymorph.
If you look at the statblock of a cat or a black bear it says "beast", so it would be allowed.
Common points of confusion
Don't confuse the spell polymorph with the spell true polymorph, because true polymorph has no such creature type restrictions on its transformation. It is also a 9th-level spell, so your wizard will not be casting it any time soon.
Druids have an ability somewhat similar to polymorph called Wild Shape. However, like polymorph, it can only be used to transform into beasts. There are other differences between the spell and the druid feature as well, but those are unimportant for this question as long as you understand they are separate things.