Its obvious that we are all wrong and the truth is that Ultimecia is Squall. I will now present the S=U theory.
Ultimecia is actually Squall in the future who forever punishes himself due to his lack of strength and in ability to protect anyone. Ultimecia's true goal is not Time Compression as much as its to keep "himself" in an eternal time loop.
The proof is that Ultimecia never directly tries to kill Squall when hshe had the chance on several occasions when he possessed Edea and Rinoa. Ultemacia also chooses to create Griever from Squall's mind and use its power, Ultimecia being actually Squall would also believe that Griever is the Ultimate GF and thus creates him to crush Squall's hope since Ultemacia knows how to screw with his head.
The wings Ultimecia uses are also a refernce to each of the witches that Squall faces, he wears two wings on the back to represent Rinoa, their gnarled and long wingspan represents the similarities to Adel's and the black feathers are from the feathers adorned on Edea's dress. Thus his design is an inspiration from the wing symbolism common in all the witches in the game.
Ultimecia's final lines in her/his ultimate form are also evidence.
Reflect on your...
Childhood...
Your sensations...
Your words...
Your emnotions...
Time...
it will not wait...
no matter...
...how hard you hold on...
It escapes you...
In my theory its obvious that this line is directed at Squall as a last ditch effort to try and make Squall into Ultemacia eventually and continue the time loop of punishment that he created for himself. He asks himself to reflect upon his childhood where he was abonadoned by his father and "big sister" and lost his mother. A childhood that fuels Squall's anti-social behaviour and self loathing. The very elements that personify Ultemacia her/himslef.
How does Squall become a Sorceror/Sorceress?
The ending sequence of the game in which Squall visits his past self and gives Edea the idea of SeeD shows through her dialogue that any of the children could accept the power. Squall gained his power from Rinoa in an alternate timeline in which he doesn't save her. This is presented in the sequence of the ending's dream in which Rinoa's suit breaks in outer space. This is not an illusion caused by Time Compression but rather Squall reliving the memory of the alternate timeline in which he doesn't save her. This leads to his emotional breakdown at the end cause he finally realizes the truth that he is the cause of everyone's misery. Its only When Rinoa saves him that he is able to finally forgive himself.
How did Squall get into the future?
Obviously, Squall was sealed away perhaps by his own will in the cryo freezer Esthar created. In the games Timeline (we'll call it T2 since its the secondary timeline and T1 will be the alternate timeline), Rinoa is sealed away but Squall is the only one who comes and rescues her, which leads us to believe that the others would not be so inclined to save Squall of whom the party has a much rockier relationship with than Rinoa. This is how Squall is able to make it to the future, and beat the "human lifespan' issue of the Ultimania.
Why does he seek to destroy the past?
His frozen slumber is not enough to punish him and eventually Squall falls into depression and madness over the guilt of not saving Rinoa. He instead chooses to punish himslef, to do this he must utilize Time compression to keep an eternal time loop. Time travel is normally impossible but through Time compression, Ultemacia can skip through the "folded"pockets of time and directly affect things. Ultemacia, creates the scenario to lead up to Squall's eventually failure and eventual acquisition of power. He possesses Edea and starts the Galbadia conflict, eventually possessing Rinoa to keep his future self from harm and to place Rinoa in mortal danger that will lead to her death and Squall gaining her powers. After Squall is frozen, Ultemacia possesses Ellone and starts Time Compression which allows Ultemacia to travel back in time and tell Edea about SeeDs. This is why Ultemacia appears at the same place as Squall in the ending cause its the place Ultemacia has to directly affect except in the ending time has been altered.
Why not directly control Squall or Ellone?
Due to the butterfly effect, Ultimecia must be careful not to enter his own body. Though he may have lived the life, memory is a funny a thing. In order to keep his own existence as Ultimecia a reality, he cannot take the chance to alter Squall's feeling more than he should. Thus Ultimecia only indirectly affect Squall by putting pressure on him and placing Rinoa and the others in danger. Ultimecia already knows how Squall will react regardless of the situation and as long as it fuels his anger and inadequecy then Ultemacia's existene is safe to continually punish himself.
Ellone is more for the Time Compression itself and he does eventually possess her but only after reaching the events in which S becomes U.
Why a woman?
Partially to hide his identity, but looking at Squall's past and general psychology, its obvious he has the traits of a man who has Image dissociation. He hates woman yet idolizes them. In the dialogue, he is generally meaner to Rinoa, Quistis, and Selphie. More so than other woman in the game. He only seems to idolize his "big sister". From his past, we see he has abandonement issues concerning women and that they always seemed more powerful to him. The few sorceress' he met are strong willed women. Even Quistis and Rinoa prove to be rather bossy types that force him to go along and with Squall's desire to be strong, does it not seem obvious he would choose a woman to be the ultimate form of power when becomes omnipotent.
Through the poers shown of changing Edea's appearance to bringing thought to life, its obvious that its not impossible for Squall to change his appearance. Though it must be noted that Ultimecia reatins the feathered ruffles from his bomber jacket on his dress in her alternate form. He changed the color from white to black in order to signify his fall from grace.
Why does time change in the course of the game?
This is partially due to the butterfly effect. Squall obviously cannot control every factor and obviously screwing with the space/time continuum would result in minor factors changing that eventually lead to Squall finally succeeding in rescuing Rinoa in space. This completely alters events and forces Ultimecia to go ahead with Time Compression to stop the party. This is very important as its the only way to save his current state before the time backlash he created changes the future. His final moments battling himself are spent not only intimidating himslef and destroying his self confidence but also to try and bring forth the elements that will lead Squall onto the road of becoming Ultimecia. This is reflected in Ultimecia's final words. Even though he's killed, Squall still goes along with his noraml plan and uses Time Compression to visit Edea in the past except it also launches the past Squall to the same moment. The past Squall tells Edea about SeeD but his future self in its dead and limited capacity is only able to transfer his powers to Edea instead of his past self.