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>I agree. Things should be as they are. However, I disagree in this case. In the English language it is awkward to consistently write sentences which are designed for gender-neutral applications. Using "they" or "their" has gained traction because people want a gender-neutral approach to their writings, and not just to be politically correct, but because it accurately addresses their target audience.
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There is a word for gender neutral addresses already: ONE

... if one presses the button, one gets to the ....

No need to invent more words, especially since the average person uses only about 500 out of tens of thousand in any give language.

Also English speakers don't learn grammar anymore in school, unfortunately.
the gender in a language has nothing to do with sex. eg. in German it is die Blume (female) and der Baum (male) and both can be BOTH male or female in real life :-)