Eobard Thawne, better known as Reverse Flash, didn't originally set out to kill Barry Allen's mother. His actual target was Barry Allen himself. He planned to eliminate Barry in order to erase the existence of The Flash, his formidable adversary. However, this initial plan was thwarted when The Flash followed him through the speed force, a dimension accessible to speedsters, and secured his younger self to safety.
Infuriated by this failure, Thawne quickly improvised a new strategy. He aimed to alter the course of events in such a way that Barry Allen would never acquire his super speed and become The Flash. Thawne believed that the traumatic experience of losing his mother would deter Barry from his destined path. Therefore, he made the drastic decision to kill Barry's mother.
Yet, in a turn of events, Thawne found himself unable to return to his own timeline after committing this act. He discovered that he had lost his connection to the speed force, which was crucial for his time-traveling abilities. This led to an ironic twist: in order to restore his connection to the speed force and return to his timeline, Thawne himself had to ensure that Barry Allen became The Flash.
This entangled series of events showcases the complex dynamics between Barry Allen and Eobard Thawne, and the drastic measures Thawne took in his mission to eliminate The Flash, only to find himself in a situation where he was forced to create him.