The Renegade is a thorn is Paige's side, but he's also a little more than that.
The more time goes by, the more apparent it becomes that he isn't actually trying to hurt her, even when they fight. (That's one of the reasons she's almost certain he isn't Tron. He isn't angry enough, not violent enough. He doesn't derez other programs.) That doesn't mean he isn't dangerous- he's still causing chaos across Argon- but credit where credit is due, for every time he blows something up, he also makes sure she's out of the blast radius. The Renegade saves her more often than he puts her in danger; but she knows why that is.
He's trying to wear her down.
"You could join me," he offers, every time her team betrays her or leaves her behind, every time he stops her from falling to her death, or pulls her to safety from some disaster he caused. There's always a nano where he doesn't seem like the enemy, then- when there's a different warning somewhere in her core. He's holding her hands or touching her back- too close. His voice is low and warm, and some traitorous part of her thinks that staying in his arms isn't a terrible idea.
Paige usually responds by shoving the Renegade back into whatever mess he pulled her out of, saying something along the lines of, "Not interested, thank you," as she watches him fall.
This doesn't deter him, though, because he has no sense of self preservation. No matter how high the fall or how brutal the hit, the Renegade always comes back; still tries to help her. To turn her.
She's not sure which one of them he's going to get derezzed first.