The premise is that Kou has poor people skill. This is what caused her first job as an AD, what makes her oblivious to Rin's feeling, etc. It's not only anime logic, it stays within the mindset of Kou.
Perhaps a case of low confidence? Or perhaps, Kou is well aware of how it would impact Rin and that is why she hesitates to tell her. Judging by how she took Nene's reflection, she is afraid of how Rin will react and I can imagine that the reason why she doesn't tell her right away is that Rin would probably try to stop her, or so would Kou think, and maybe she thinks Rin is capable of making her changer her mind.
That said, Kou doesn't realise that doing something behind a friend's back is more upsetting than actually leaving them, because as a good friends they would support you. So yeah, I think it boils down to Kou being kind of oblivious to/bad at social interaction.