This question makes me laugh because there are so many answers I could put here. I guess I could have been predictable and answered Kyon/Koizumi, Shinagawa/Izumi, Zoro/Sanji, Roy/Ed, KakaIru, et cetera, but I chose this one because even the staff made fun of this pairings' popularity. Also, I hate one of the characters in this pairing, but in terms of the pairing itself, I don't actually hate it so much as I don't understand its wildfire popularity. Which is different from the other pairings that I listed above, more or less. -_-
( Day 28: A pairing that you will never understand? [I smile every time I see the LOVE statue outside my work because of Episode 24.] )
I feel like my answer to every question in this meme was either a HELL YES or a SHIT NO, with no middle ground. Good job, meme creator.