The second simple answer from the article is basically this: pointing out that A is conditionally defined in step 1, but both definitions are used in later steps as if they are the same value. It then goes on to over-explain that a bit, but this answer is in there.
I agree with you. What I am taking issue with is the article presenting a multitude of (unnecessarily) complex refutations (as if one wasn't enough) and suggesting that there is no consensus on which one should be believed. This is not how people do mathematics!
A better article would first introduce a more precise version of the switching argument and then precisely identify the flaw in it. The more advanced mathematical and philosophical discussion that explores variations of the basic argument should be separated and contextualized clearly.
