I was asked the same to prove parental responsibility. Not sure why they did that. I had two child-renewal applications, one went through with just the old passport, the other required the birth certificate as additional supporting documentation (my name is on the certificate and was married at time of birth). I didn’t want to chance it, so I also included a letter of ‘no objection’ from my wife, although they said to send one or the other.
I remember one main difference between the two renewal applications. The one that didn’t require additional supporting documents was in a regular, manual queue, whereas the other one was in what I understood is called the ‘digital queue’ (tracking ending with the letter X). Also, each application was assigned to a different passport office (I made them a few weeks apart).
I seem to recall that in my case, it took about a week after the additional documents were delivered for the application to be approved. I also don’t think I received confirmation of receipt for the certificate (nor did it show in the application tracking).
Hope your application gets sorted soon!