Earlier quoted context omitted.
He digs into his marriage a lot more in later blog posts: https://matthewfray.com/an-open-letter-to-shitty-husbands/ . I don't think she used it as an excuse at all, but he's more using this one frequent occurrence as a metaphor for the marriage.
To be honest, it feels like a lot of the descriptions of the volumes on that page are strawmen or cherry picked bad examples. Nobody gets divorced for leaving a dish by the sink. They might get divorced because they just don't do anything around the house (aka unequal distribution of work/chores).
To him, a single glass by the sink was no big deal if there was no company. She didn't want the glass by the sink. Him refusing to even consider a compromise here was communicating "what you think is important doesn't matter."
My wife is one of those people that thrives on a regular bedtime schedule (always go to bed at X PM, every day). I'm the sort of person who goes to bet at 9pm one day, 2am the next, but I always get up at the same time.
So far, all good.
However, she really wants me in bed next to her if we are both home. I think this is silly. It was a constant fight for a while until we had a couple of good talks about it; she sleeps just fine with a light on, so I can have a book or a laptop[1] in bed next to her and be awake as long as I want and she is perfectly happy; me being a voracious reader am also pretty darn happy with this. Also, had we not talked this out, this solution would never have occurred to me; I can't fall asleep with a light on in the room unless I am seriously sleep deprived. At first I was reading only e-books on my phone to not disturb her, but when I mentioned that to her she said "oh I don't mind a light on."
Perhaps in the author's example, if he thought he might want another more water before running the dishwasher, there might be another place he could put his water glass that his wife would be fine with. Maybe she'd even be happy to check there and put it in the dishwasher before running it! Maybe he'd have just had to come to terms with "We got 12 glasses at at our wedding and there's only 3 people in the house, so I can just get another glass." We will never know because these conversations just didn't happen.
1: The laptop I reserve for emergencies only; I really don't want to do anything even slightly work related in bed, if at all possible.