(quoting from the wikia)
According to the Final Fantasy VIII Ultimania, Ultimecia's actions are driven mostly by a means to escape her destined defeat at the hands of this "Legendary SeeD." Ultimecia's knowledge of this fate could be the main instigation for her desire of bringing about the phenomenon of Time Compression, by which all time would merge. Through the Time Compression spell, Ultimecia could absorb all time, space, and existence, thus becoming "a living god," incapable of dying. With this power, Ultimecia would be completely omnipotent, and could control all time, space, and existence, effectively preventing her fated demise.
It is made clear from her inauguration speech in Deling City that she has suffered through intense persecution. Future generations were aware of the coming of Ultimecia because of her failure to complete Time Compression. They likely reacted by targeting all sorceresses for persecution and isolation, because of the fear that any one of them could eventually become the "cold-blooded tyrant" that Ultimecia speaks of.
Ultimecia was condemned for crimes she had not even committed yet. This prejudice and condemnation (and perhaps the actions that spawn from such states) is perhaps what prompted her into becoming a wrathful sorceress. Sadly, it is through Ultimecia's desire to alter time and escape her fated persecution and defeat that the terms of her destiny are fulfilled. Her downfall at the hands of Squall Leonhart and his comrades perpetuates the cycle that will lead to the formation of SeeD and the continued persecution of Sorceresses unto her era.