That is not what people mean when they say "you're my opposite".
They are not implying that "they're all there, and you're not".
It's usually intended as nothing more than the observation that two people have a pattern of having notably differing opinions on an assortment of topics, and nothing else. It's not intended as a jab or an insult. It's not meant to be taken absolutely literally, and applied to everything, including implying that they're sane and you're crazy, etc.
It is a common phrase between two people where one person likes horror but the other likes comedy, one likes dark colors and the other likes bright colors, one likes spicy food and the other likes sweet, one is a bit of a pessimist the other more of an optimist, "they're total opposites!" is all that means - in no way is it meant to imply that one is better than the other.
The "profound" nature of the comment is just cos they've realized the pattern in that moment, not cos it makes them feel like some kinda deep philosopher or something. It's just recognizing a pattern. I thought it was pretty common to have an "oh!" moment when one notices or realizes something they hadn't before, no matter how mundane.
The reason for the comparison to themselves isn't "banality" or that they think they're the golden standard of something - just that they are the one person they know best, and - just like everyone else - they're inherently going to see the world from their own eyes. It doesn't mean that they see themselves as the ideal to be compared to, just that they're comparing two different things - one of which happens to be the inherent lens they see the world though. It's just a comparison, not a judgement.
The reason your comment "left him speechless" is cos in the typical context, it didn't make any sense.
I can't help but wonder from what source you got your interpretation, or how you came to your conclusion.