It's always irritated me to see the use of the word "her" because of the blatant political-correctness of it. If you want to be PC, use "their".
So we can only use "his" or "their"?
constantly using "their" when reading anything that remotely resembles a story gets old pretty fast.
You don't like implied political correctness. OP doesn't like implied gender bias. I don't like grammatical convolutions like using "their". What's to be done?
How about focusing on the message?
> what's to be done?
use "their"
Then use 'their'.
This particular (hypothetical) startup founder happens to be singular, and female.
That's the exact opposite of the situation. I pointed out that the founder is singular and female, but the "singular they" is used for indeterminate number and/or gender.