If you want to talk about a generic person or a person whose gender you don't know, you have several options.
You can consistently use "he", which will annoy some people. Technically the sentence "Man is an animal that bears live young; he is pregnant for about nine months." It looks awful, and you probably wouldn't use it for that one, but you can.
You can use "she" consistently. Not much better.
You can alternate "she" and "he" or use whichever makes the most sense. Of course, then your personal biases will tend to show through, and it can make for confusing writing.
You can use "he/she", "s/he" or some other hybrid. This tends to be awkward, and makes for clunky writing.
You can use newly invented terms for this like "zie" or "je". This can be confusing, and will irritate many readers.
You can use "it". That's a lot of fun, but will sound weird and really annoy many people.
You can use "they", which used to be a valid use of the term, but now leads to sentences that are considered ungrammatical.
You can give up and try to word all of your sentences in the third person plural. This is hard to do.
We really could use a good agreed upon solution. Currently, you just have to find the method that works best for your writing and particular audience. But it's a stupid problem to have.
Discussion (7)
they is considered grammatically correct by linguists in terms of modern common usage.
Claims inspired by this comment
"they [used as a gender-neutral third person singular pronoun] is considered grammatically correct by linguists in terms of modern common usage." - Cobra BaghdadSure, and if I'm writing to linguists then I'd happily use "they". But I studied technical writing, and that means writing to many different audiences. If you piss of your audience, you don't accomplish your goal. And many people don't accept "they" in the singular. Which means we need a commonly agreed upon usage, which we don't have. Not everyone is a linguist.
French grammar states that the male gender overrides the female gender for a subject involving both. When your mother tongue has such a rule, you never perceive it as sexist. Also, this is helped by the fact that words have genders and that genders seem randomly distributed. Word genders and sex are orthogonal (masculine/feminine and male/female).
French may be fine as it is, but English could use some help.
"they" is fine as is. If someone doesn't like it, they are unsupported by common usage and they are ignoring a perfectly good solution to the problems outlined in this claim.
bignose, but people who don't like it hold power. So, you can say piss off if you don't like it, but you can also get badly hurt doing that.
I'm approaching this from the viewpoint of a technical writer, where money and respect hang in the balance. And that sucks, because it's stupid. Get everyone to agree on "they" and that's fine. But pick "they" and you have to defend your choice as various people who didn't get the memo that it's okay write in to complain.
in the meantime, I'll keep saying "their" and making grammar nazis cringe