Cycling as a sport for children?

I'm not sure if this is the right subreddit; if I'm wrong, I apologize. English is not my native language. I live in Europe.

My daughter is 8 years old, and my husband would like to introduce her to cycling as a sport. We spoke to some local organizations. Mtb, road and gravel are offered. My husband advocates "road" as if there were no room for discussion.

My husband has an old mountain bike (I'd say entry-level? 15 years ago we paid €350 for it). He rides regularly, but he's not one of those people who ride for hours every weekend. He doesn't watch cycling on TV (actually, he doesn't follow any sports on TV), but only reads about it online. So I'm still surprised about his preference.

I'm very scared of the possible risks. I'm afraid my daughter will get hurt. I have the feeling (wrong?) that road cycling is much more dangerous than mtb. I'm also worried about...you know...but my husband says it's not that world anymore.

Can anyone reassure me that it's a healthy and safe sport?
My daughter has a mountain bike but she is also attracted to the road ones. Should I push for mtb? Or could gravel be a compromise?