It tricked me the first time I saw an opponent use it, but basically it all comes down to colon placement.

Discarding is part of the cost to activate the ability, but tapping is not.

So you don't have to be able to tap it to make it indestructible, and therefore it doesn't have to be tapped to activate the ability.

the card is written to make someone think that tapping it while its untapped it part of the cost, and therefore it shouldnt be able to become indestructible if its only tapped. you jerks shouldnt be writing cards that are purposely confusing! shouldnt need to have a supreme court hearing to figure out how a card is supposed to work. if the tapping is not part of the cost then put that part last, in a new sentence, and put something like "tap it if its uptapped" so there is no confusion. you act like it costs you extra money to print extra letters. be verbose you fools! by the way this card is super over powered if you can tap it while its already tapped.