"Wash hands of" — why not "off" instead of "of"?

Question

The phrase "wash hands of" is supposed to mean giving up or having nothing to do with something.

But why is it "of" and not "off"? Using "off" sounds more like giving it up and distancing oneself from the object/subject.

Answer 1

In the words of the Oxford English Dictionary,

After transitive verbs, the person or thing affected (‘secondary object’) is often introduced by of.

Of represents what was in earlier stages of the language a genitive. Other verbs which have this feature include cheat, defraud, accuse, suspect and avail.

Answer 2

The significance of the preposition of is brought out well in the definition here:

Verb
to wash one's hands of
1. (idiomatic) To absolve oneself of responsibility or future blame for; to refuse to have any further involvement with.

[emphasis on of is mine]
See also: 'dispose of', 'get rid of'

I have no conscience, none, but I would not like to bring a soul into this world. When it sinned and when it suffered something like a dead hand would fall on me,—"You did it, you, for your own pleasure you created this thing! See your work!" If it lived to be eighty it would always hang like a millstone round my neck, have the right to demand good from me, and curse me for its sorrow. A parent is only like to God: if his work turns out bad so much the worse for him; he dare not wash his hands of it. Time and years can never bring the day when you can say to your child, "Soul, what have I to do with you?" — Olive Schreiner [dictionary.com quotes]