Be very critical of accepting odd bits of talk, brooking no argument (6)
I believe the answer is:
flatly
'brooking no argument' is the definition.
I can't tell whether this defines the answer.
'be very critical of accepting odd bits of talk' is the wordplay.
'be very critical of' becomes 'flay' (I can't justify this - if you can you should give a lot more credence to this answer).
'accepting' means one lot of letters goes inside another.
'odd bits of' means one should take alternating letters.
The alternate letters of 'talk' are 'tl'.
'flay' going around 'tl' is 'FLATLY'.
Can you help me to learn more?
(Other definitions for flatly that I've seen before include "Absolutely" , "point-blank" , "Categorically" , "in uninspiring fashion" , "(Deny) without qualification" .)