The most common and most likely answer to this crossword clue is the 7 letter word ILLOGIC
I've seen this crossword clue in The Guardian
I
L
L
O
G
I
C
More clues leading to the result ILLOGIC
- Wrongly attempt to back current Conservative leader — it makes no sense
- Senselessness of sick needing oxygen getting rolled-up cigarette
- Bad good? One senior officer’s admitting this doesn’t make sense
- Bad soldier stops officer in charge retiring — it doesn’t make sense
- Wickedness long since hiding every other craziness
- Senselessness of the Italian in charge defending record
Buddy explains!

The straight part
We know that "it makes no sense" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case it makes no sense = illogic.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does ILLOGIC mean?
ILLOGIC noun- Lack of logic; unreasonableness; a fallacy.
- Contrary to logic; lacking sense or sound reasoning.