Deep-Seated

Properly used, this idiom, meaning well established, is spelled as shown in the title. Deep-seeded, an uncommon malapropism, may stem from the false notion that deeper seeds are better rooted than shallower ones. The correct idiomatic term, deep-seated, originates in horseback riding, where sitting deep in the seat means to sink the rider’s weight into the saddle and be firmly established on a horse.