"I CAN'T!" Bossy heartless ridiculous pigheadedness (9)
I believe the answer is:
obstinacy
'pigheadedness' is the definition.
('obstinacy' can be a synonym of 'pigheadedness')
'i can't bossy heartless ridiculous' is the wordplay.
'heartless' suggests removing the centre.
'ridiculous' is an anagram indicator.
'bossy' with its middle taken out is 'bosy'.
'i'+'cant'+'bosy'='icantbosy'
'icantbosy' is an anagram of 'OBSTINACY'.
(Other definitions for obstinacy that I've seen before include "Stubbornness" , "character of mule" , "Pig-headedness" .)