Show off vs. show up?

[Thameem]

English Language Proficiency Tests, Advanced Level

ESL/EFL Test #75 "At the End of the Day (4)", question 9

give the rest of the house a surprise by showing ......... your classical education and say:

(a) up
(b) on
(c) off
(d) in

English Language Proficiency Tests, Advanced Level

ESL/EFL Test #75 "At the End of the Day (4)", answer 9

give the rest of the house a surprise by showing off your classical education and say:

Correct answer: (c) off

Your answer was: incorrect
give the rest of the house a surprise by showing up your classical education and say:
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Why Off ? why showing up does not correct for this sentence? Please explain

[Mister Micawber]

show off = proudly display
show up = appear
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Native English teacher at Mister Micawber's