himself, herself, and themselves

There are some aspects of the English language that I find completely absurd. To elaborate, I recently discovered that "themselves" is not a real word. It's just a pretend word. Yet, everyone I know - myself included - uses this word. The rule, apparently, is that sine the plural does not exist, you have to say "himself" or "herself". So, in this sentence: "my neighbors went to the market, and they bought themselves some fresh mangoes", the word has been used incorrectly and it would instead have to say "bought himself and herself". Or something like that.