As a GUN agent, Shadow needs to recapture Toffee and detain her, but he is entirely in the dark about who she is, and why. Due to how relentless the pursuit is, Toffee resents him and tries to weasel her way out of recapture in any way possible, and eventually comes to loathe him. Above all else she does not want to go back to jail.
Eventually through Rouge and Sonic, Shadow gains an understanding of who she is, but unlike them, he does not trust her and has no conflict over following his orders to recapture and detain her.
When Toffee finally learns his name, she manages to recall the info she learnt about him, and turns to bargaining with him through a call for empathy, which eventually develops into a desire to turn him to be against GUN. She conflicts him with a call to his inner loneliness by pointing out she would be the only person he’ll ever meet who truly understands him - that they are the same.
He eventually becomes knowledgeable of his past, but does not remember it directly. His understanding changes his course from working with GUN, but he has a calmer attitude. He believes Toffee can change and tries to sway her away from pointless revenge, but she is still unwilling to change.