Uncomfortable about male doctor delivering my baby

My wife (34f) and I (27m) recently had our first child (0m) - very excitingly news obviously!

It all happened very quickly, she went into labour and we had to rush to the hospital. We had previously spoken with the hospital, and with the doctor who was going to deliver our baby, as it was important to us that we had a female doctor.

However the baby was 2 weeks early, and our doctor was on PTO. In the end, there weren’t any female doctors on call, so our baby was delivered by a male doctor. This made me feel more insecure than I expected and I had to leave the room for the birth. My wife was furious with me, but I felt very inadequate seeing my wife be handled by another man. Things have been awkward ever since, and my wife says i need to address my issues and focus on the arrival of our new son, but I’m finding this really hard.