Good question, I think I would move the rook
Question about puzzle

There is a small magnifying glass icon at the bottom left corner of the position. That leads you to engine analysis.
In such positions usually you'd hope that the knight won't be able to leave the corner. Then you'd be down an exchange instead of a full piece on c1. In the position after Nxa1 white can play Nd2 and make it difficult for black to get the knight out, possibly trapping it later with moves like b3/b4 and Bb2 and Rc1 if the knight moves to c2.

Basically it is what everyone has said. On top of that, imagine what happens if you move the rook. You lose a piece for free and after that your rook is somewhat misplaced, plus that pesky knight remains alive and is an active piece. So just by understanding that, you will understand that giving up an exchange is a better option (but of course black is winning in any case).

Well, you are correct because the fork is devastating itself and is the entire point of the puzzle. In a real game if you figure out that the fork will give you some material no matter what, you wouldn't look much further.
But I think that it can still be an interesting exercise in evaluating a position (do you try to save a rook or keep developing), so figuring out the answers to questions like this one could help OP get better in the long run.
Hi I was wondering why white didn't move the rook instead of moving the knight?