Why did brinker resign as president of the Golden Fleece Debating Society?

Brinker resigned because he couldn't enlist.

If he could not enlist—and for all his self-sufficiency Brinker could not do much without company—he could at least cease to be so multifariously civilian. So he resigned the presidency of the Golden Fleece Debating Society, stopped writing his school spirit column for the newspaper, dropped the chairmanship of the Underprivileged Local Children subcommittee of the Good Samaritan Confraternity, stilled his baritone in the chapel choir, and even, in his most impressive burst of irresponsibility, resigned from the Student Advisory Committee to the Headmaster’s Discretionary Benevolent Fund. His well-bred clothes had disappeared; these days he wore khaki pants supported by a garrison belt, and boots which rattled when he walked.