It’s an old post, but it’s a good one: a master post of arguments for using singular ‘they’ as a gender-neutral pronoun in English.
Gabe Doyle (the author of this post) does a pretty good job of collecting and explaining just why people who use singular ‘they’ should not be set on fire immediately. This includes everything from a list of famous authors who have used this form (gasp!), to grammar books that suggest that ‘they’ is acceptable as a singular noun, to syntactic number agreement, to sociolinguistic and sociocultural understandings of gender.
It’s something I like to point out as an example whenever someone learns I’m a linguist and thinks I’m about to go all grammar commando on them: I use singular ‘they’ a lot, and not just in speech but in my writing as well (casual and formal). And if you stop and think about it, you do too; and we don’t care about number agreements or syntax or what the dictionary says. It’s just something we say, and we make it work and it only stops working once you try to apply arcane, institutional rules to it.
What does that say about those rules, hm?