Chess.com Analysis says Kc1 is the best move, but it isn't...

I wouldn't know how to program a chess computer, but I would expect it to be able to identify the 1 out of 3 moves available that does not lead to losing a Queen or Mate in 1.  My human opponent found it.

Is there something I am missing or do not understand?  This is move 25; does the analysis stop working at move 20?  Do I stop trusting the post game analysis, or am I just not seeing something?

All moves available led to mate. However, mate takes longer after Kc1 (10 moves) than after Kd3 (6 moves) or Kd1 (1 move).

Therefore, it does not seem inaccurate for the computer to recommend Kc1 as best.

Ok, so its looking further into the future than me.  Good to know.