The most common and most likely answer to this crossword clue is the 5 letter word SCRAP
I've seen this crossword clue in The Times
S
C
R
A
P
Buddy explains!

The straight part
We know that "Cancel/fight" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case cancel/fight = scrap.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 SCRAP mean?
SCRAP noun- A (small) piece; a fragment; a detached, incomplete portion.
- (usually in the plural) Leftover food.
- The crisp substance that remains after drying out animal fat.
- Discarded objects (especially metal) that may be dismantled to recover their constituent materials, junk.
- (in the plural) A piece of deep-fried batter left over from frying fish, sometimes sold with chips.
- A Hispanic criminal, especially a Mexican or one affiliated with the Norte gang.
- A snare for catching birds.
- To discard.
- (of a project or plan) To stop working on indefinitely.
- To scrapbook; to create scrapbooks.
- To dispose of at a scrapyard.
- To make into scrap.
- A fight, tussle, skirmish.
- To fight