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SIngular they never fell out of usage, but it was considered non-standard English dialect for about three hundred years. Standard formal grammar rules from the 18th century until the last quarter of the 20th defaulted to he/him where gender was unknown or irrelevant. Singular they was grudgingly accepted as standard about ten years ago. Until then, every major style guide forbade singular they in favor of "he or she" or recasting the sentence to avoid pronouns altogether or to semantically justify plural they. Other languages have either found their own solutions or decided that their traditions are good enough and kept them.

Personally, I just avoid pronouns whenever possible, especially if someone is likely to throw a tantrum over an honest mistake due to a lifetime of custom. I've never been particularly upset at singular they, but I also don't take offense if someone follows the older formal grammar rules either.