Don't think anyone answered this for you. (Actually Hope totally did, but I digress.
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) Well, it was based on several things.
Basically it all starts with the plot of Disk 1 and the inherent ambiguity of the game's optional dialogue. Aerith is (literally) first on the scene and immediately starts making bold moves on Cloud. And players who prefer Aerith make dialogue choices which, combined with scenes that are stereotypically trappings of romantic interplay, make it seem clear that Cloud and Aerith are falling in love.
Players who didn't make those dialogue choices obviously took issue with this; hence, the LTD was born. Neither side could really claim optional dialogue as real proof of romance, and so the debate shifted to focus on non-optional plot. This is where CxA began to circle the toilet bowl. The game's plot twist on Disk 2 makes all of Cloud's actions in Disk 1 suspect; at the same time, a very clear and powerful story arc between Cloud and Tifa begins to emerge, fleshed out by the scene in the Lifestream and capped by the Night under the Highwind. CxA isn't left with much to work with, except for a scene where Cloud accepts an outreaching hand in the Lifestream and says "I think I can meet her... there." And, the fact that nowhere in the game does Cloud specifically say "I love you" to anyone.
At this point things got really nutty. The CxA side began organizing a set of talking points based on "evidence" having nothing to do with the plot. Most of it had to do with some very... nebulous symbolism and Japanese culture. Other points included Cloud and Aerith's cameo appearances in other games, Tifa's absence from the early drafts of the game, Aerith's prominence in the game and high visibility in advertising, and comparisons with "canon" couples found in other FF games. A website called Destiny Fulfilled, a CxA shrine, went whole-hog with this angle, writing essays on topics such as the number of displays of affection Cloud shows to either girl.
The hilarity that ensued from these "proofs" being presented seriously is the stuff of legend.