"some kids don't adapt well when a solution doesn't go exactly as planned. Mike, a remarkably rigid thirteen year old, had agreed with his mother over when (12 noon on Saturday) and how (with her help) he'd clean his room."
Unsurprisingly, Mike can't do it by himself; he requires organizational assistance. Then, mom was an hour and a half late and without preamble, wanted to start doing it at that point. No evidence in the text that she called him at 11:45 to renegotiate because she was about to be late to her appointment with him, which is of course what Well Behaved Adults Do in a world of cell phones, and even before that if they were somewhere with access to a phone. I'm assuming the Mike family home has a phone.
They fight. Duh. If you're an hour and a half late without telling me, even odds I won't ever speak to you again because You Are Unreliable (obvs, if you are in the hospital, lost cell phone, etc. then I'll rethink it, but I'm going to expect an apology, minimum, modulo hospital/unconsciousness/sufficiently major other surprise disaster. It is just not that hard to let someone know you are going to be late). Does the author characterize this situation as a parental error? Nope.
"What Mike needed was a complete renegotiation of the original agreement. He was just that rigid."
Well, _yeah_ he needed a complete renegotiation. She totally blew him off. That's not being rigid.