The main reason for that is Tifa was a last minute addition to the game. She was, at first, fan service. They re-wrote Aeris's plot, gave Tifa Aeris's old plot(Aeris was originally planned to have Tifa's role in the game as Cloud's childhood friend), and set about filling in some gaps. It took time away from the reviving Aeris function and multiple ending developments, so Tifa could be seen as partially ruining the FFVII game. But now we're used to their roles, it's hard to imagine how the game would've turned out without Tifa.
And the actual scenario is:
Aeris: 50
Tifa: 30
Yuffie: 10
Barret: 0
The character with the highest points by the second Gold Saucer trip goes on the date with Cloud.
Aeris's point system was originally planned to serve a second purpose. If you got her points high enough(100% of points available for her, or near to it), in Disc 3 you would've been given the option to revive her, and unlocked a second ending. However this was never completed.
In short, Squaresoft developed FFVII with the classic 'only one option' scenario in most FFs(Squall x Rinoa, FFVIII, Zidane x Sara/Dagger/Garnet, FFIX, Tidus x Yuna, FFX, Cecil x Rosa, FFIV). But, by adding in Tifa, reasonably well I have to admit, they created a scenario that is one of the key debates in the FF fanzone, who does Cloud love?
The biggest argument is that by which part of Cloud is it that cares for who? As anyone who has gotten far in the game will know[spoil]Cloud's mind is made mostly of Zack's[/spoil] so his feelings for Aeris [spoil]could be seen as those of Zack's[/spoil]. However, when he discovers himself again[spoil]after falling into the Lifestream and being saved by Tifa[/spoil] he begans to show his feelings for Tifa, and reveals that at the start, before he joined SOLDIER, he did have strong feelings for her. Now depending on the date mechanic once more, if you go with Aeris, she says something like:
"I finally get to see the real you" on the date.
Now some could see this that she has seen the Cloud he has forgotten, and does care for that Cloud more than Zack. However, whether that Cloud cares for her I don't know, as I haven't played the game through with him caring for her the most.
If you play through it with Tifa the highest, you get the following quote:
[spoil]"Hey Tifa......I......there are a lot of things I wanted to talk to you about. But now that we're together like this, I don't know what to say...I guess nothing's changed at all...Kind of makes you want to laugh...[/spoil]
This can clearly be seen as him saying that he still feels about her as he once did, if stronger.
But of course, this all ties back to the mechanic. No matter how much one is encouraged by the mechanic, as long as the option is there, all four shippings can and should really be seen as equally canon.
This eventually boils down to preferences. No matter what you say, 'that the game supports *whatever*', it all ties down to how you play the game, and which character you like more, or how much you understand the mechanic.
It's a story you have choice in writing. By giving you that choice, no single hint is 100% both sided.
But, as I said earlier, I like Tifa x Cloud, because the romantic plot they share on Tifa peferance playthrough is brilliant in my opinion. Not because the game hints 'whatever', but because by my preferances, I found a plot I like.