18 is really a no-brainer but is 16-18 that different? Maybe it is, I don't feel I was a lot different!
I’d not let a child decide whether to join us or not.
What it boils down to is that some people regard a 16-year-old as a child whereas others think they are essentially adults.
In my experience (and I have discussed this with other professionals), girls do a huge amount of growing up between the ages of 13 and 14. Boys tend to be a little later (it's in the immediate post-puberty period). By 16 they are at about the same level and the increase in maturity during the next two years is pretty minimal.
The age of majority was 21 until 1970, when it was lowered to 18. I doubt whether it will be lowered further because the United Nations Convention on the Rights of the Child confers additional protection to those who are legally children. This does not mean they are children in any practical sense, and 16-year-olds do, in fact, have some adult rights. (For example, living independently, passports, medical consent - and in some parts of Britain, voting.)
I think most reasonable parents wouldn’t be supporting a sixteen year old to move out.
Surely this depends on the context. We supported DS2 to move out so he could do the exact course he wanted at one of the few schools that offered it. Was that not reasonable? But most 16-year-olds appreciate what a bargain it is, living with parents and letting them pay the bills. I suspect those that do want to leave may have unreasonable parents.
I'd discuss why they don't want to go and if it's valid, explain why they can't just be left alone
It would be interesting to hear your explanation. Do you think they would agree with you? As I see it, the end product of parenting is an independent adult. Treating someone like a child until they turn 18 is, I think, unlikely to achieve that.