Michelle, I have a child built along similar lines-- so I do understand that.
The thing is this-- when it's going WELL, my DD would always say that she saw the benefit in such activities and understood why not quitting them was important (piano, in her case)-- but when it was NOT going well was definitely not the time to ask and hope for a rational or well-considered response.
She has also differentiated between creative/expressive endeavors and those which are procedurally demanding-- the former, she can afford to be 'giddy' and kind of Tigger-ish (her term) about those things. Things like her latest efforts as a librettist, adaptations of plays, and designing, discussing literature, that kind of thing. She lights up from the inside and it bubbles out of her.
On the other hand, math isn't like that. She does talk about math, but not with the same glowing, energized excitement that she has for musical theater. But it doesn't mean that she loves it any less. It means that she needs a different kind of mental discipline in her approach to mathematics (and piano, too)-- one that doesn't allow for "giddy" until she has mastered the basic tools with which to fly.
She's just now developing that kind of metacognition, though-- and she's 15.
I thought that was a great insight. We DID "force" her to do math at a level that seemed reasonably like a compromise between what she'd have preferred (never learning anything new) and what we thought was technically "right" (at least another year of acceleration, probably two)-- but we never made her enter competitions, force her to work with a tutor, etc. etc.
I'd have a sincere conversation with the child in question and find out if s/he can appreciate that the decision to pursue afterschooling is one that is in his/her best interests. Or not.
DD came down on the "it's better the way it is" side every time-- and the one time she didn't, we listened.
