Crossword Genius

Supports people have when annoyed (5,2)

Ross

I believe the answer is:

backs up

I'm a little stuck... Click here to teach me more about this clue!

'supports' is the definition.
('back up' can be a synonym of 'support')

'people have when annoyed' is the wordplay.
I cannot quite understand how this works, but
'people' could be 'backs' (back is a kind of person) and 'backs' is present in the answer.
The remaining letters 'up' is a valid word which might be clued in a way I don't understand.
This explanation may well be incorrect...

Can you help me to learn more?

(Other definitions for backs up that I've seen before include "Supports" , "Stands by" , "what annoying people get" .)

I've seen this clue in The Globe and Mail.
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