I do understand why I'm wearing cycling pants all the time. I'm totally used to the pockets in my back of my jerseys and jackets. I understand where my gloves and helmet help. And I could continue going through my wardrobe but there's one more thing I'm seeing all the time: Socks. What's so special about road cycling socks compared to other socks? Ok, they have to make sure my feet don't swim in sweat, but that's no specialty over other kinds. What else?
If it's about other riders laughing at me when I'm on my road bike, well, I can live with that. I simply laugh at them when they finish the track -- just when I'm done showering. ;-)
Just one thing I didn't see addressed in the other answers: Cycling shoes are very low-volume - which means they are supposed to fit very snugly and not have a lot of room for your foot to move around. This is why cycling specific socks are so thin - they are designed to maximize moisture transfer off of your foot (to keep your feet comfortable) while not creating extra pressure due to extra material and/or padding.
Plus they're usually slathered with brand names and they match the rest of your kit. So, they're totally necessary if you're going to look pro. And as we all know, looking pro directly translates into going faster ;-).