Breeding timing in songbirds usually tracks the spring flush of caterpillars, which is when insectivorous nestlings can be raised most efficiently. Goldfinches feed their young an almost entirely seed-based diet, so their constraint is different. They wait for composites in the aster family to set seed and to release pappus, the fine fibre attached to the seed.
Both halves of the timing are practical. The seeds feed the nestlings, and the pappus lines the nest cup, which the female weaves tightly enough that it can hold water. Nesting usually starts in late June or July, well after most local songbirds have fledged their first brood.
The seed diet has one striking consequence. Brown-headed cowbirds sometimes lay in goldfinch nests, but cowbird chicks reared on a goldfinch's seed diet rarely survive, so the nest is a poor host for the parasite. The related belief that goldfinches turn a different colour by moulting into new yellow feathers is correct: they undergo a complete moult in autumn and a body moult in spring, unusual among finches.