Question

Why is the move "present" so strong for Delibird?

Answer 1

Its strong when you actually manage to hit 120 base power.
Present has a chance of being 40 base power, 80 base power, 120 base power, or healing the opponent.
You probably experienced it at 120 base power. And that's how GameFreak wanted it.

Answer 2

A move doesnt get stronger when a certain Pokemon uses it. The only thing that powers up moves is STAB,Items,Stat Modifiers, and Abilities. Delibird doesnt receive STAB so thats not it. It could be holding a item, or its ability Hustle, which raises Attack but lowers Accuracy. Maybe it had its Attack at a +1,+2,+3,+4,+5, or +6.

Summary:
Delibird will only cause a huge amount of damage with Present is if it has a item to boost the damage, it has Stat Modifiers, or its Ability Hustle is in effect.