Discarding a card is part of the ability’s effect and isn’t optional. As the cohort ability resolves, if you have a card in your hand, you must discard one, even if the card you may have wanted to discard as you activated the ability is no longer in your hand.

To activate a cohort ability, the Ally with that ability must have been under your control continuously since the beginning of your most recent turn. Informally, it can’t have “summoning sickness.” However, the other Ally you tap can be one that just came under your control. (Note that tapping the second Ally doesn’t use [the tap symbol].)