"Both of them share feelings for Cloud -- Tifa was close to Aerith, who can also be called a love rival. With that point in mind, they were also good friends. Nevertheless, it is not hard to imagine that she carries complex feelings as a woman toward Aerith, who had built up a special bond with Cloud that was different from Tifa's.
Tifa's complicated feelings continue even in AC, two years after Aerith had departed the world.
This was due to the fact that Cloud, succumbing to the notion that Aerith's death was his fault and condemning himself, construed that Denzel was 'the child which Aerith brought here' and took care of him. In addition, Cloud had also gone away to the church that Aerith had been in.
The thing which she is unable to hide in her irritation towards Cloud is the fact that he isn't merely dragging the past around, but because that reason might perhaps be related to Aerith." -10th anniversary ultimania