ASK DOCTOR DOROTHY PASTENSE FULLSTOP:
Why do you use 'they' as a neutral or, to be more precise, genderless, pronoun in the book? It is 'he', and always has been. The use of 'they' is a recent thing.
And, of course, a whole host of quotes can be used to 'prove' the point. Just type in the words 'he who...' or 'he that'...' in Google, and you'll get a whole raft of quotes where 'he' could be interpreted as a neutral pronoun. Many of these lines - 'he who' or 'that' or 'which' and so on - can have their origins traced as far back as the Bible. Here's a couple of examples where the use of he is being used as a generic pronoun:
"And it shall come to pass, that he who fleeth from the noise of the fear shall fall into the pit; and he that cometh up out of the midst of the pit shall be taken in the snare: for the windows from on high are open, and the foundations of the earth do shake." - Isaiah 24:18
He that sacrificeth unto any god, save unto the LORD only, he shall be utterly destroyed. - Exodus 22:20
It is probably true to say that he as a generic pronoun was quite popular until fairly recently.
But look at this example (courtesy of Steven Pinker): Everyone (each individual) returned to his seat. The problem is that this suggests that the entire group of people returned to the one seat. It would be clearer to say everyone returned to their seat.
The use of they and them as a third-person pronoun and their as a possessive pronoun has been around for a long time. Here's an example where if you want to avoid the word 'them', you will have to rewrite the sentence, but it would be rather difficult:
Julie interviewed everyone before the human resources manager spoke to them.
If we had to follow the 'rules', shouldn't we be saying 'him'? The pronoun is talking about the group and not Julie. I think you'd agree that would be rather silly to say Julie interviewed everyone before the human resources manager spoke to him.
They and their as third-person neutral pronouns when referring to groups of people are perfectly acceptable.
We now live in a modern society. These days there have been a lot of changes in the social world, sexual discrimination is - quite rightly - no longer tolerated, and many women have become very successful and have advanced in society. These days using he or his is used to refer to someone male and not a generic pronoun. There may be those that consider the use of he/his as an appropriate pronoun for both sexes when the gender is not mentioned, but makes it clear that the group includes women; some see this as treating a woman like a second-class citizen.
When TEE was being put together, there was a conscious decision to use only neutral (or genderless) pronouns - they/them - when giving such examples in the book. It was considered inappropriate and incorrect to use he/him/his for a neutral pronoun. Plus, of course, it would avoid any possible problems that the examples above would give.
If the author has slipped in a he/his pronoun where they or their should be, then he (the writer is male) apologises.