Polymorph (4th level spell) is limited in what it can turn things into.
From the spell text (second paragraph) :
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). The target’s game statistics, including mental
ability scores, are replaced by the statistics of the chosen beast. It
retains its alignment and personality.
A beast is a particular creature type. The creature type is listed in the stat block of a creature. Compare adult red dragon (dragon) with allosaurus(beast).
Beasts are nonhumanoid creatures that are a natural part of the fantasy ecology. Some of them have magical powers, but most are unintelligent and lack any society or language. Beasts include all varieties of ordinary animals, dinosaurs, and giant versions of animals. (SRD p. 254; DM Basic Rules p. 2).
Other types include fiend, fey, dragon, aberration, celestial, construct, monstrosity, ooze, and humanoid. Unless the creature form chosen is a beast (allosaurus, brown bear, etc) the 4th level polymorph spell won't do the trick.
As far as the game is concerned, a dragon is not a beast; a dragon is its own type of creature.
Dragons are large reptilian creatures of ancient origin and tremendous
power. True dragons, including the good metallic dragons and the evil
chromatic dragons, are highly intelligent and have innate magic. Also
in this category are creatures distantly related to true dragons, but
less powerful, less intelligent, and less magical, such as wyverns and
pseudodragons. (SRD p. 254 ; DM Basic Rules, p. 2).
The 9th level spell, True Polymorph, has no such restriction.
Creature into Creature. If you turn a creature into another kind of creature, the new form can be any kind you choose whose challenge rating is equal to or less than the target’s (or its level, if the target doesn’t have a challenge rating). The target’s game statistics, including mental ability scores, are replaced by the statistics of the new form. It retains its alignment and personality.
Your friend may be confusing the two spells, or may not quite see the distinction between creature types. On a humorous note, @NathanS suggests that the most powerful choices for the 4th level polymorph spell are Godzilla (T-Rex, CR 8, beast) or King Kong (Giant Ape, CR 7, beast). How does the character feel about being polymorphed into one of those magnificent beasts? :)