Thanks for your reply, @PollyPeachum. Genitals can be malformed at birth, just like any other body part. The most usual developmental abnormality is cleft palate, where the two halves of the face haven't fully joined up in utero.
One fairly common abnormality in genitals is quite similar - hypospadias. This is where the penis develops off-centre so, instead of the tube running down to middle to exit at the end, the urethra exits somewhere along the underside of the penis. In severe cases the urethral opening forms a slit down the length. It's estimated that about one in 200 boys are born with hypospadias.
In some girl babies, the clitoris is larger than normal (clitoromegaly). It can be caused in utero by a number of hormonal issues or vitamin deficiency. Some of these girls have puffy labia at birth.
At first glance on delivery, a boy with hypospadias might be taken for a girl, and a girl with clitoromegaly might be thought a boy. In the past, this has led to children being raised as the opposite sex. You'd think the presence or absence of a vagina would give a clue, and I really don't understand why this happened.
From roughly the 1960s onwards, surgeons became able to 'correct' some of the abnormalities. They did this to boys with hypospadias by removing the testes, then stitching everything together so the genitalia resembled a vulva, and creating a false vagina! The surgical reasoning was that the boy would never be able to urinate like a man but, by making it all lie flat, he could pee sitting down like a woman. These children were then told they were girls.
As those children grew up and puberty didn't happen, they were understandably shocked to learn the truth. They eventually formed groups, finding other people who'd been born with unusual sex organs, and started campaigning. They want to improve understanding about differences/disorders of sexual development, and to stop the practice of summarily changing a child's supposed sex.
You can see why they're so cross about genderists claiming to share the same issues and borrowing their language ("assigned at birth"). "Feeling like" the opposite sex is nothing like finding out as a teenager that your body is not the sex you've been told it was, that you've been irreversibly altered by a surgeon, or that you've got a developmental difference which may affect your future sex life and fertility.