When a speaker is making a determination about something in Japanese, the 副詞（ふくし） (adverb) むしろ is often used to express a more accurate depiction of what has already been said. This is regularly translated as ‘rather’, or ‘instead’.
むしろ will mostly appear at the beginning of new sentences, or the beginning of a second clause within a sentence, before information about (A) will clarified.
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何（なん）でそっちが怒（おこ）ってるの？むしろこっちが怒（おこ）りたいよ。
Why are you mad? I want to be the one that is mad instead. (It would be preferable if I was mad, because you’re the one that is wrong)
むしろ、安（やす）い方（ほう）を買（か）った方（ほう）がいいとおもう。
Buying a cheaper one would be better instead.
As むしろ seeks to give a more accurate description about something, it will often be paired with grammar patterns such as より, to show where the comparison is being made.
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車（くるま）をリースするより、むしろ中古（ちゅうこ）の車（くるま）を買（か）った方（ほう）が安（やす）く済（す）む。
Instead of leasing a car, it would be cheaper if you bought a used one.
俺（おれ）はMMOよりよりむしろシングルプレイヤーのゲームの方（ほう）が好（す）きだ。
Rather than MMOs, I like single player games more.
むしろ comes from the kanji 寧（むし）ろ, literally meaning ‘preferable’. This is the same kanji that appears in the word 丁寧（ていねい）, meaning ‘polite’ (sometimes also translated as ‘careful’). The grammar structure むしろ itself may even be translated as ‘preferably’, simply expressing that careful consideration has been given to describing something accurately.
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むしろ、そっちに謝（あやま）ってほしいよ。
Preferably, I want you to apologize. (Rather than me, it would be better if you apologized)
むしろ、先生（せんせい）に聞（き）いてみた方（ほう）がいいんじゃない？
Preferably, wouldn't it be better to ask the teacher? (The teacher will give a much more preferable answer than me)