Hurry up fielding strange question, giving illogical answer (3,8)
I believe the answer is:
non sequitur
'illogical answer' is the definition.
'hurry up fielding strange question' is the wordplay.
'hurry' becomes 'run' (running is a kind of hurrying).
'up' says the letters should be written backwards (in down clue: letters go upwards).
'fielding' indicates putting letters inside (field can mean catch).
'strange' indicates an anagram.
'run' back-to-front is 'nur'.
'question' with letters rearranged gives 'onsequit'.
'nur' going around 'onsequit' is 'NON-SEQUITUR'.
'giving' acts as a link.
(Other definitions for non sequitur that I've seen before include "Conclusion that does not connect with the previous argument" , "Something not following on logically" , "Illogical conclusion" , "Conclusion that doesn't logically follow" , "Statement not expected" .)