counting captures

In the lesson titled "counting captures" at 5:00 we are told that capturing with the rook is best. This makes no sense to me. He is left with a knight, a less valuable piece, instead of his rook. Why is this being touted as the best move?

I don't think it said capturing with the rook was better. The lesson explains that because black only has a rook left defending the bishop, so capturing with either the rook or the knight works out for white.  If he takes the bishop with the rook, it would be an equal trade if black then traded the rooks.

I think they should teach take with the knight. It's obviously the better move. Especially since the lesson is teaching about the value of pieces.

I don't see the difference here. If you take with the knight, he won't capture your knight with his rook. So material value will be the same (rook knight vs rook knight). If you took with rook and he capture back, material value still the same (knight vs knight). In both scenario, you still end up with 1 extra pawn. Lesser piece on the board will simplify the position and usually advantageous to the player with extra pawn.

Taking with Rook is also more natural move as u usually dont want to pin your own piece (altho both move is ok in this position).

I do not see any good reason to pick one capture over the other.

Objectively, both captures should be equally strong but actually taking with the rook is slightly more appealing, as if Black swaps rooks the resulting knight and pawn ending is extremely problematic for Black, while if Black moves away the rook then it's rather obvious that d5 is a great central square for my rook.

I'm not sure I agree.  

It's a good principle for pure beginners, but also something you need to unlearn later.  Both cases win a pawn, you shouldn't be afraid to increase the pressure by taking with the more valuable piece.

You're right. I didn't think of that and incorrectly assumed he would.