Drawing a card is not optional. You must draw 1 card any time "Airknight Parshath" inflicts Battle Damage to the opponent’s Life Points. This includes direct attacks, and when it battles with a monster with a lower ATK or DEF.
If the opponent activates "Waboku" or "Kuriboh" to reduce the Battle Damage to 0, you do not draw.
When "Airknight Parshath" attacks a face-down monster with a Flip Effect and inflicts Battle Damage, you draw 1 card before the Flip Effect is applied.