Can't move past c section

I planned an all natural birth with a water labor. Well at 42 weeks still no baby so the midwife wanted me induced, which meant no water labor. Baby's heart rate dropped, I needed emergency c section. She's perfectly fine and healthy but I just can't bring myself to say "she was born". I have to say "when she came out" or something like that. I just don't feel like I've given birth. As a woman, my body completely failed me. I didn't go into labor on my own, and I didn't finish on my own. How do I move past this? It's like one minute I was pregnant and then there was a baby. I feel like I seriously failed and I'm really upset about it