That's called a disagreement. Everyone has them. We all experience moments like that.

Have you reversed the situation? They share a view, you share an opposing view. Neither you nor they are budging, or even attempting to hear the others views. You're both just giving your view. Yet you interpret that as not being heard or listened to, but you don't see it as you doing the same to them. Yet they don't see your not accepting their stance as suggesting they aren't being listened to.
The only real difference is that you take it personally if they are that way to you, but they don't take it personal when you do it to them.

And since you so easily back down you encourage their behavior of being dismissive of you. Not taking things so personally and being willing to stand firm could change things, though it will take a long time.