別に～ない【べつに～ない】

別に in front of a negative means "not particularly", "not really": it plays down whatever follows. The verb or adjective after it is negative – a ない-form, an い-adjective in 〜くない, or じゃない after a noun or な-adjective.

Without the negative, 別に is an ordinary adverb meaning "separately".

別に on its own

As a reply, 別に stands alone and the negative is understood. It brushes the question off, and said flatly it sounds cold, close to English "nothing" or "whatever". To a teacher or a customer, give the full polite sentence instead.

"It's not like…"

With わけじゃない at the end, 別に denies a reason or a motive the listener might read into something.