Dislike admitting son’s rashness (5)
I believe the answer is:
haste
'rashness' is the definition.
(I've seen this in another clue)
'dislike admitting son's' is the wordplay.
'dislike' becomes 'hate' (to hate is to dislike strongly).
'admitting' indicates putting letters inside (admit can mean to welcome in or accept).
'hate' placed around 's' is 'HASTE'.
(Other definitions for haste that I've seen before include "Rapidity" , "Hurriedness" , "Expeditiousness" , "velocity" , "go at speed" .)