Filthy was just me being cheeky, but I did fall out of favor with the Clerith ship because the compilation (the movie & CC prequel) fleshed out Zack and Aerith's relationship. I didn't play CC, so I can't comment on that; however, I did follow it at arms-length and it seemed to me to be the more natural pairing since they were both the chipper type and are now both in the Lifestream. I believed in a lot of the points that the author of the Clerith page spent excruciating detail debunking (e.g. likes Zack, never knew real Cloud, etc.).
This was compounded by a recent fanfic I read that supported that pairing ('cuz Cloud jumps back in time when they were both alive and tries to kill Sephiroth). Add to the fact that Tifa is awesome, and CloTi seemed to lend itself into existence.
Keep in mind it's been many years since I played the game AND I wasn't in the frame of mind to catch all those details. But I critically examined that essay and it raises a lot of good points with sufficient evidence to back it up. I'm a logical guy and I like it when claims are substantiated. Obviously you can't talk about love logically, so at the end of the day what got to me was how much Cloud cared about Aerith (way more than I thought) and how much Aerith cared about Cloud (way more than I thought). My initial reading of the game and the characters were superficial. I didn't have thoughts much more complex than "oh, she's interested" and "hey, he seems interested".
When you see things like, "If this smile costs only one gil, it is a good purchase," or "but Cloud is Cloud. I, now undoubtedly, love Cloud much more than Zack," (ouch, sorry Zack) or "seeing Cloud and Aerith developing their world together," (ouch, sorry Tifa), it tugs at my heart strings in all those intangible ways.
Regarding Tifa, I agree with the author's assertion that Cloud and Tifa are (less) compatible with each other despite the author's ridiculous anti-Tifa bias. They're going to need WAY more work to make the relationship work because both are introverted, closed-off, and needing a strong emotional bulwark to support them. I'm not saying it's impossible, but it doesn't come as naturally as Aerith who has enough emotional gumption to support the both of them. Make no bones about it, Cloud acts downright rude to Tifa in the OG game ('til she reconstructs his identity), in Case of Tifa (compilation shenanigans), in ACC (compilation shenanigans), and in KH2 (hrm...). At times it seems borderline one-sided and Tifa has to keep inserting her presence into his perspective less she falls behind.