Rinoa and her father could never see eye to eye, the ideals that he represented were the absolute opposite to Rinoa, and she probably knew that considering she got her stubborn side from her father, there would be nothing she could do to convince him of her ideals otherwise. Rinoa left for a reason, she probably had tried numerous times to convince him to see things the way she does, but her father is not the type to be swayed by emotion. He's a general, a military man.
Going by character, General Caraway looks like the type of serious father who left all the coddling and nurturing to the mother. It's obvious that he does care for her, but he's the type to put work first, family second. I'm sure Rinoa was aware of this too, and it's obvious the two of them weren't close anyway.
Rinoa made her own family with the forest owls and now she has made a bunch of true friends along with Squall who is loyal to the point that he would turn on the world to stop harm from coming to her, who needs a dad like her's when she's got a guy like Squall? She's still an impulsive teen, whose to say she won't make up with her father later when she's older?
It's more realistic this way, instead of resolving issues with her dad for the sake of a cliche' ending.
