I stick to no younger than 16 for chemical services.
As above, all instructions on hair colour (inc. box dyes) state they are not to be used on persons under 16 yrs so if you ignore the manufacturers advice, your insurer won’t cover you in the event of a claim.
I know it’s hard as many youngsters start experimenting with colour in their early teens but I think 11 is far too young and I would definitely discourage them as their body is growing rapidly and you really don’t know if the chemicals used could cause them harm at some point. Anecdotally, I’m aware of the increase in people who I know becoming allergic to substances that was pretty much unheard of 30 plus years ago, so I tend to be cautious where children are concerned.
If you are being put under pressure and don’t wish to do it, just say that your insurance won’t cover you as that’s perfectly true.