How and why did American kids become dinosaurs enthusiasts?

Although the context is slightly different, you may find my answer to this question, Why did kids all over North America want to be a marine biologist in the 1990s?, interesting. (Be sure to check this post from /u/kelpie-cat which gets into the popularity of whales.) Your question is also related to the history behind asking children about their favorite color.

In effect, it's a feedback loop. American adults have long asked children about their favorite thing and/or encouraged hobbies and collections and at various moments in time, different things have been children's "favorite", which leads to adults encouraging an interest in children in that thing. Individual adults often remember a particular thing that was the start of their interest, usually related to pop culture, but it's rarely one thing (except for fad toys and each one of those has its own history) that puts something on the radar for children.