"It's a woman thing"
Some readers will have a ready explanation for the habit, and it's that women apologise more and they're a woman and there's nothing to be done about a fact like that.
Go back to Schumann and Ross in chapter 4, because the study was designed to test exactly this, and what it found is more precise than the stereotype and more useful. Women in the diary study did apologise more. They also recorded committing more offences, and the proportion of offences that got an apology was the same for men and women. Nobody was apologising more readily. Women were counting more of what they did as an offence, and men were rating the same behaviours as less severe. The difference was in the threshold, not in the willingness to say sorry once the threshold was crossed.
I want to be careful here, because the book has made no other claim about gender and won't. The study is one study, of a few hundred people, in one country, and it's about diaries and hypothetical offences rather than doorways. What I take from it is narrow. If there is a difference, the research locates it in the threshold, in what gets counted as a fault, and the threshold is a judgement and judgements move. A person who's been told they apologise because of what they are has been given a reason to think the habit is fixed. The study says it isn't. It says the habit is a count, and the count can be recounted.
So "it's a woman thing" may describe an average and it doesn't describe a fate. Men who count everything as a fault apologise all day too, and there are plenty of them in every office. Women who don't, don't. The method in chapter 20 is a recount, one day's sorries sorted into fault and not, and the recount works on anyone whose threshold has drifted low, whoever they are and whatever they were told they'd be.
And if you want one more reason not to accept the explanation, it's that it's a sorry in disguise. "Sorry, it's a woman thing" is an apology for apologising, and you've apologised enough.