How exactly does a father pass down moves?

Question

If, for example, I breed a male gyarados that does not know twister with a female salamence, will the resulting bagon learn twister or does the gyarados have to know the move?

Answer 1

No

Gyarados must know twister in order to pass down the move. Gyarados can learn twister at lv. 29.

Level up the gyarados to lv 29, have it learn twister
Breed it with a female bagon or any of its evolutions.

The resulting bagon will know twister.

source: knowledge

Answer 2

>The way the Pokémon inherits moves are based solely upon the base form's own learnset. The parents that need to know the moves are as follows;
Moves in baby's Level Up: Both Parents
TM Moves: Father (pre-XY)
Egg Moves: Father
Move Tutor Moves: Cannot be bred

The Gyarados must know Twister in order to pass it down to the offspring.

In X/Y the mother can also pass down egg moves.
>As of Pokémon X & Y, it's now also possible for the mother to pass Egg Moves down. If the mother has one of the Egg Moves of the baby, it will pass the move down.

Source

Hope I helped.