How can I improve my listening skills to better respond to opponents' arguments?

Well. The first thing you have to do to be more receptive is stop with this antagonistic framing.

That is - when you refer to ANYONE you are engaged in discourse with, civil or otherwise as an ‘opponent’ and you refer to the discourse as an ‘argument’ - this, in a literal sense - shuts down your brain to hear ANYTHING OTHER than evidence to substantiate your position and undermine theirs.

Over time this develops filters and censors, making it nigh impossible to actually comprehend their perspective - and you adopt this belief that chipping away at one single element of their story will completely invalidate them and their story but you’ll refuse to apply the same rules to you and yours.

For those attempting to explain something. You’re perceived as antagonistic - since we know - with your laser focus on a single element that doesn’t make sense to you of our story is your focus. And we KNOW you’re not actually listening, but you’re only listening to prolong and/or win the argument.

Which places people you’re conversing with into oppositional positions.

So. The first step is. Fix your mindset.

Unless you’re in a courtroom, the person you’re discussing things with who may have a different perspective is NOT an opponent. They are merely someone with a different perspective than yours which from their perspective quite likely is equally as rational as yours is. The way you perceive your discourse PARTNER is of utmost importance in hearing about and learning about their perspective with an open mind.

Understand that their perspective can and likely is NOT OPEN FOR DEBATE. While it may not appear this way to someone who is antagonistic in nature like I presume you to be with the nature of this question, most people don’t want to argue - particularly when they’re sharing how they perceive the world, their beliefs, the future they want for this world, their recollection of events and experiences, etc, etc. Now keep this in mind as you ARGUE for your position. You’re pushing your beliefs onto someone and forcefully trying to get them to agree with you and your perspective. That’s very disrespectful to do, and let’s be real - you’re not winning anything when someone agrees to go along with you simply to get you to leave. All they really want to do is close the door on you and be done. Not the best way to win friends and influence people by invalidating them and their perspective in favor of your own, is it?

The WORDS YOU USE to FRAME your discussion MATTERS. When you regard a conversation as a debate and a perspective as a position, You cannot help but naturally build up defensive filters to eliminate any noise to the contrary of your perspective, believing it to be a position, which in many cases makes it impossible for you to grow and learn as a person. These filters you develop over time are HARD to eliminate and take years of work to shatter ONCE you recognize they’re there. They shape your world in ways that appear beneficial at first, but in the end - you realize an argument is an addiction and you’ve won nothing when you are more interested in shutting people down than you are learning about your world. Fix that framing now. Unless you’re playing a game or in a competition - stop referring to ANYONE you’re conversing with as an opponent. They are NOT.