Why not "on" and why "off"?

[Leonid]

English Language Proficiency Tests, Advanced Level

ESL/EFL Test #41 "Talking through his hat", question 1

I do take my hat ......... to the new director for having pulled the company back from bankruptcy.

(a) by
(b) on
(c) to
(d) off

English Language Proficiency Tests, Advanced Level

ESL/EFL Test #41 "Talking through his hat", answer 1

I do take my hat off to the new director for having pulled the company back from bankruptcy.

Correct answer: (d) off

Your answer was: incorrect
I do take my hat on to the new director for having pulled the company back from bankruptcy.
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Let me know why not "on" and why "off"?

Leonid

[Alan]

Hi Leonid,

Take your hat off means remove your hat from your head. Take your hat off to someone is an expression meaning congratulate.

Alan
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English as a Second Language
You can read my ESL story A day in the life of a policeman