Could you explain what does it mean?
I didn`t mean to push all your buttons. I was just looking mute.

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What is the situation?

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As I see it: I didn’t want to get you annoyed, I just wanted you to stop talking.

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Maybe "I was just looking for the mute ...?" That's the button which turns off all the sound - the mute button, often called just the mute>

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Pushing someone's buttons means to try to aggravate or annoy someone. As far as the last sentence I am not sure.