I am tired of having this argument over and over again on Twitter, and IRC, and mailing lists.
There is no excuse for unnecessarily gendered language. Specifically, the lack of a good pronoun in English is not an excuse. English has a gender-neutral sentient pronoun: they/them/theirs.
Your inability to understand the subtleties of subject/verb/object agreement in English does not trump the fact that it is offensive to assume that everyone is a man.
Even if your grammatical objections were valid, they are not worth making someone feel excluded over. This is a value judgement: you are not excused for making someone feel marginalized, unimportant, unwelcome, and awkward just because some phrasing sounds odd to you.
But, let me assure you, those objections are not valid. They are based on historical misunderstandings about the differences between Latin and English, by overzealously prescriptivist grammarians, literally all of whom were men.
For one example of why the "problem" with "they" is not actually a problem - i.e. the fact that it is semantically singular but morphologically plural - consider that there's another word you're quite familiar with that has this property: English's second-person pronoun, "you". English used to have a distinct, singular second-person pronoun, "thou".
While Wikipedia does note that there is still "some controversy", that does not mean that the controversy is at all valid. The linguistic pedigree of the singular "they" is near to a millennium long at this point. Far more famous, far better writers than you have used this construction to great success.
As Joan Taber put it:
"[History] is not on the side of those who would ban singular they from written texts; neither is logic; nor is majority rule."
So, if you go on using "he", "him", "his" to describe a hypothetical person (and, given the audience here, probably a hypothetical programmer), you're demonstrating two things to me:
Therefore, go, and sin no more: when want to describe someone (not "a man"), refer to them as "them" (not "him").
And, if it grates on your ear a little each time, just remember that, by doing so, you are being nice, and that is a better thing than sounding nice.
P.S.: If you still insist on pseudo-latinate prescriptivist grammatical dogmatism, but are still sensitive to the gender-neutral language issue and prefer to use some nonsense like Spivak, I will still think you're a bit daft. However, that's a clear improvement upon the alternative, which is for me to think you're rude and inconsiderate.