Exactly.

The mage casts Chill Touch, just to spite you.

It’s probably because whenever spellcasters are being compared, a Wizard comes in and says something like “we’re the only ones who had to work for our magic”, as if finding a powerful entity and convincing it to make a not horribly skewed bargain, learning to commune with the land itself, or following the orders given by a deity isn’t “work”.

And don’t Bards also have to study their magic?