My kids both learned to knit at school when they were 7. They went to a Waldorf school and knitting (well, handwork in general) is a big part of the curriculum.
They begin by teaching finger knitting in the early childhood and then having the children make their own needles from dowels and begin to knit in the first grade. That said, there are kids who can only make a tangled mess of their work for the first year and others who pick it up quickly. I still have the rather odd shaped piece of knitting that was my son's first work somewhere around.
I would guess that most kids can get the hang of working with knitting needles around the age of 7 but agree that it depends on the child and their level of interest as to whether they'll stick with it or not.
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