On (the gender of) my hypothetical reader

In my writings, I used to virtually always refer to my hypothetical reader as “he”. The reasons for doing so were actually very well explained by none other than Richard Dawkins, in his great book The Blind Watchmaker.¹ Here is the relevant passage, from that book’s preface:

I am distressed to find that some women friends (fortunately not many) treat the use of the impersonal masculine pronoun as if it showed intention to exclude them. If there were any excluding to be done (happily there isn’t) I think I would sooner exclude men, but when I once tentatively tried referring to my abstract reader as ‘she’, a feminist denounced me for patronizing condescension: I ought to say ‘he-or-she’, and ‘his-or-her’. That is easy to do if you don’t care about language, but then if you don’t care about language you don’t deserve readers of either sex. Here, I have returned to the normal conventions of English pronouns. I may refer to the ‘reader’ as ‘he’, but I no more think of my readers as specifically male than a French speaker thinks of a table as female. As a matter of fact I believe I do, more often than not, think of my readers as female, but that is my personal affair and I’d hate to think that such considerations impinged on how I use my native language.²

My native language is Portuguese, where a similar convention also exists. And moreover, in my view Dawkins’ reasoning applies to both languages—which is why I used to follow Dawkins' strategy, i.e., always refer to the reader as male. However, I know think that a better alternative is to do both, that is, to refer to said reader both as a male and as female—just not at the same time! That is, instead of resorting to those ghastly "he-or-she" or "his-or-her" linguistic horrors, I do either one or the other, more or less at random. Happy readings!