Drink problem or drinking problem

Test No. [color=blue]incompl/advan-64 “Pay and Allowances”, question 2

Although he knew it was a sensitive subject, his boss had to ask him the question about his drink problem.

(a) sincere
(b) fragile
(c) breakable
(d) delicate

Test No. [color=blue]incompl/advan-64 “Pay and Allowances”, answer 2

Although he knew it was a sensitive subject, his boss had to ask him the delicate question about his drink problem.

Correct answer: (d) delicate

Your answer was: [color=green]correct
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Can we also say “drinking problem”? or are these different?

I guess a drink problem is as bad as a drinking problem.[YSaerTTEW443543]

TOEIC listening, photographs: Machu Picchu, Peru[YSaerTTEW443543]

What is “delicate question”?
What does the sentence mean?

thanks

Drink problem has become prevalent in the UK over the past 30-40 years, but grammatically only the gerund drinking can be used as an adjective (type of problem) or even if reworded, a noun for an activity (problem with drinking). For anyone outside the UK “drink problem” would refer to a situation in which something is wrong with your drink (say a fly in your Coke or whiskey in your vodka tonic).

@Zhang

In this case delicate means something that could likely make the person uncomfortable or embarrased.