Our DM was saying that an Arcane Trickster Rogue casting a Firebolt does not get the sneak attack damage on a hit. Is that right?
Spells cannot be used for sneak attacks....
... unless the spell involves making a weapon attack as part of its action, such as Greenflame-Blade and Booming Blade, in which case, you can apply sneak damage.
Sneak Attack (PHB Pg. 96)
Once per turn, you can deal extra 1d6 damage to one creature you hit with an attack if you have advantage on the attack roll. The attack must use a finesse or a ranged weapon.
The rules for sneak attack state:
The attack must use a finesse or a ranged weapon.
A spell is not a finesse weapon, nor is it a ranged weapon, so no sneak attack damage can be applied from casting it.