There are some great detailed answers behind the 12/13 age limit below, which discuss the disadvantages of not knowing the effects owing to the lack of testing (rightly so) done on kids, especially that of Harshal Kolambe (हर्षल कोळंबे). Further, they cover the legal aspects too.

Another area we should discuss involves the physical issues:

the head strap won’t fit securely on a young person's head
distance to lenses
distance between lenses
size of the headset would mostly cover a child's face rather than sit on the nose
These additional reasons make it uncomfortable, will likely heighten one's chances of getting sick, the vision blurriness associated with lens distances will most likely increase the chance of eyestrain and headaches, and further kids’ brains don’t fully understand the nuances of VR versus the real world and so are more likely to walk straight into a physical wall, object, sit on an imaginary couch, etc.

In summary, the core issues are lack of testing/knowledge, consequently, the likes of Oculus, Vive, and other headset makers are to cater to a larger audience.

I own lots of headsets and have allowed my kids to go into VR worlds. In general, I have found that google cardboard VR headsets and spin-offs, which involve using one's phone cater the best to young audiences. However, as James Carter suggests, if you do allow kids in, just limit their use to as short as possible, and ensure they take regular breaks without extended use.

Here’s a related video of my daughter and a friend trying out a headset for the first time. It shows how they perceive issues, asks about their environments and highlights what a lot of fun it can be. Looking forward, I sincerely hope there are no issues with kids and their use, especially in short-term usage, as the benefits to education could be huge.

PS I couldn’t upload the video, so had to go with a GIF, yet hopefully, you can still see the excitement and intrigue