Angry, anglers about a critical point (10)
I believe the answer is:
crossroads
'critical point' is the definition.
('crossroads' can be a synonym of 'critical point')
'angry anglers about a' is the wordplay.
'angry' becomes 'cross' (I've seen this before).
'anglers' becomes 'rods' (rod can refer to a person who angles).
'about' is an insertion indicator.
'rods' going around 'a' is 'roads'.
'cross'+'roads'='CROSSROADS'
(Other definitions for crossroads that I've seen before include "Soap once" , "critical situation?" , "Meeting of ways" , "Intersection of ways" .)