Full-form 肉 sits at the bottom (rather than the usual ⺼ side-form) and is the indexing radical. Meat under a roof spoils - the literal seed of rotten / decayed - and the radical also explains why bean curd 豆腐 is written with this character.
The slanting roof on the upper left frames 腐 as something kept indoors - a shed or storehouse. Food left under such a roof is exactly what spoils, an apt visual for the rotting and fermentation senses.
Tucked under the roof, 付 supplies the sound, shifting from fù to fǔ. The original 付 (a hand passing something) is irrelevant here - it is recruited for the rhyme that links 腐 with 府, 附 and 俯.
