I highly doubt that there's many little kids saying they're a different gender then born as, but even if they do they're kids! Kids also run around saying they're astronauts and princesses. If you ask a kid if they'd rather have a cookie now or a savings account with $1,000, a lot of them will take that cookie. Kids can't make finalized major decisions.

How would a little kids even know for sure that their gender is wrong? Because they like guy or girl things? Because they like pink vs blue? They don't know how it works.

Now if you're talking about kids meaning like 10-12 then that's the start of puberty, the most mentally unstable time of a persons life. Hormones, bullying, body changes, self conciousness, depression, anxiety, are all normal things. How can a doctor definitively say that a kid is at a good enough mental capacity to change their gender permanently? No minor is.