Speaking as a non-believer, it’s one of my favorite chapters. 1 Corinthians 13:12 reminds us that we cannot see each other perfectly, and it does so in the context of reminding us that the greatest by far of all God’s commands is to love each other. It provides us a reason to behave charitably even when our senses tell us we have an excuse not to. In fact, the King James translation doesn’t even use the word “love,” substituting “charity,” but I prefer “love” just for poetic and sentimental reasons.
ETA: and “through” is just the metaphor the author chose: after all, what we see in a mirror is neither on nor in it, so we’re not (exactly) merely looking in or at it.