It's foolish for breeding establishment to admit odd pair (6)
I believe the answer is:
stupid
'it's foolish' is the definition.
(I know that stupid are anserine)
'breeding establishment to admit odd pair' is the wordplay.
'breeding establishment' becomes 'stud' (I've seen this before).
'to admit' is an insertion indicator.
'odd' indicates alternate letters.
The alternate letters of 'pair' are 'pi'.
'stud' going around 'pi' is 'STUPID'.
'for' is the link.
(Other definitions for stupid that I've seen before include "Not sensible or intelligent" , "Gormless" , "Brainless" , "Lacking wit or intelligence" , "Imbecilic" .)