I'm sorry to confess that I fell for the equivalent of Argument 1 in a similar puzzle in the past.

In terms of the current puzzle, I realized my mistake only when I realized that my state of knowledge isn't just that you're holding the Ace of Spades. I also know that you told me that you're holding the Ace of Spades, instead of some other card that you might have told me about. This knowledge introduces a new conditional probability into the Bayesian computation, which then yields the correct answer.