Why is it illegal to castle with both hands? I was watching the match between Ian Nepomniachtchi vs Hikaru Nakamura and Nakamura used both hands to castle.

Why is it illegal to castle using both hands? What's wrong with that?
The official procedure to castle is (Schiller 2003:19–20 from Wikipedia):


  first move the king with one hand and then move the rook with the same hand.


By using both hands the player can save time, as would by as using different hands for moving (like promoting a pawn to queen) or moving with a hand and hitting the clock with the other.