Chess Analysis Wrong

I just had this game and the analysis told me "nice comeback win." And I was a little taken aback because if anything, I thought it was a closer game in the beginning, then I clearly stepped ahead. It also called a clearly strategic move a "blunder." 

But what really had me floored was a move my opponent made which the analysis called into question (an inaccuracy) and the "best move" would have led check in 1 and 2, and to mate quickly after. 

Here is the breakdown. Does anyone else often find errors with the analysis?

If my opp had followed the "best move", I would have Qg6+, then Qh7+. Then begin the tradeoff with the rooks and continue to dismantle the defense on the open F file. For the life of me, I cannot see the benefit of the "best move" and feel the analysis is simple wrong on this one.