別に〜ない

JLPT Level: N3
Meanings

Not really

Not particularly

It's not like ... (to be) / I don't particularly ...

Usage

別に + 〜ない

Explanation
別に〜ない is used to deny that something is particularly true or noteworthy, often downplaying one's feelings or the importance of a situation. It answers or counters an assumption or prior question with a sense of indifference or mild surprise. The nuance is closer to “not especially” or “not really” rather than a definite denial. It can soften a response that might otherwise sound blunt, and is commonly used in casual speech. Often appears with contexts like: 別に大したことない (It's not that big of a deal), 別に好きじゃない (I'm not really fond of it), or 別に関係ない (It's not relevant to me / I don't care). Note that 何も〜ない or 特に〜ない can reinforce the sense of indifference.
今日は別に忙しくもないし、早く帰ろう。
きょうはべつにいそがしくもないし、はやくかえろう。

I'm not especially busy today, so let's go home early.

別に好きじゃないけど、みんなが勧めるなら試してみる。
べつにすきじゃないけど、みんながすすめるならためしてみる。

I'm not really fond of it, but if everyone recommends it, I'll try it.

別に彼のことを悪く思っているわけではない。
べつにかれのことをわるくおもっているわけではない。

It's not that I think poorly of him, it's not really the case.