If a teacher can be taught, why can't a preacher be prought?

There is no point in looking for logic in English verbs. They derive from Germanic roots and many of their Past forms follow the pattern of the German originals.

Teach, taught, taught is an irregular verb, but preach, preached, preached is regular.

Sing, sang, sung, but ping, pinged, pinged.

Drive, drove, driven, but arrive, arrived, arrived.

Praught, surely?

(They can, praught has been in informal use since the mid 19th century.)

I don't think you can compare those two phrases