Most people try to earn listening by being right more often, or louder, or first. None of that works reliably, because listening is not granted to the most correct person in the room. It is granted to the person who has already demonstrated they listen.
That's what mirroring does. Before you make your point, repeat back what the other person said, as fairly and accurately as you can manage, no spin. 'You're worried this slips the launch by two weeks.' You are not agreeing yet. You are proving you heard it correctly. People track this closely, even when they can't name why. The room shifts the moment someone feels accurately heard, and it shifts against you the moment they sense you were waiting for your turn to talk instead of listening.
This is a mechanical habit, not a personality trait. It costs you one sentence before your actual point, and that sentence is what buys you the attention for the rest of what you say. Skip it and your argument, however correct, competes with everyone else's argument for airtime. Do it and you go first, because you've already shown the room you're not just broadcasting.
If you want to be listened to, become the person other people trust to have actually heard them. Everything else, the eloquence, the data, the timing, matters far less than that one habit.
Mirroring is repeating back what you heard as accurately and fairly as you can before responding, so people register you as someone who listens, not just someone who talks.