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"Work hard, work smart, take risks, and you'll get ahead." It's simply not true. Life is, in part, a gamble.
Yes, as you mention getting ahead financially is transient... people experience floods, fires, earthquakes, and many other setbacks. Working hard often makes us feel good about ourselves in and of itself... the work is its own intrinsic reward... individuals may be satisfied to have mastered something new... and proud of high ethics and character, friendships and healthy relationships. The things polarbear mentioned are what really matter.

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Ultimately, to the school system, the gifted kids are worth the effort, and he is not.
Advanced academics provided by a school ought not to bestow a sense of worth, favoritism or superiority (or being left behind, neglect or inferiority).

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... like most of the gifted children, he hasn't been learning anything for the past four years...
It is true that the needs of many (most?) gifted children are not well-met and unfortunately he has that in common with them.

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and has NO IDEA how to learn a new math concept. He believes math homework should be completed in under 30 seconds. They are doing pre-algebra now, and he's finally having to read his math book, but refuses. So for the first time in his life, he's getting problems wrong.
Might the introduction of new resources, possibly free accessible web resources such as Khan Academy or others, help him spark his interest in learning and struggling through material... possibly acquiring study skills and developing the growth mindset would help him to avoid underachievement if he is underachieving, and even qualify for some level of advanced academics.

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believing that nobody with any intelligence should ever have to read the book, and not doing it perfectly the first time is not good enough'.
You may wish to look at several books such as the perfectionism books listed in recent threads, see if your son may like to read and discuss... often kids will do this if parents also share similar struggles.

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I want to make sure my own daughter gets different messages: that she, too, is highly capable
The book Mindset by Carol Dweck may be of interest?

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I just wish there were a way to differentiate without my kid hearing that she's in the bottom half
Flexible cluster grouping by readiness and ability for each subject, regardless of chronological age may be a way to address this. When kids are not compared to others of their age and are on par with their clustermates they may all feel special in that the grouping is tailored to them. To use an analogy to flowers, some may bloom in the Spring, others in Summer, Autumn, or Winter. Some grow best in sun, others shade. Some need a lot of moisture, others dry conditions. One is not better than another, they can each be appreciated for their own individual beauty. By trial and error we learn how each flourishes.