He liked to keep her safe, wrapped up tight in his protective arms where no one and nothing could ever harm her. He didn't like her being in danger, tried to always keep her away from it where she would be unbothered by the knowledge of all the darkness and bad things happening out there in the world. Sometimes he had to keep things from her- didn't want her to see him as a monster like his brother- but it was all for her own good, to keep her safe. Safe from things like Damon and town councils with pitchforks and rampaging ex girlfriends with a hunger for her blood.
He tried to keep her safe from things like him. Monsters in the dark; the ones little children instinctively believe in but grow up and talk themselves out of their silly beliefs. It makes it easier to sleep at night if you can pretend not to hear every little thing that goes bump in the darkest hours. He wants that for Elena, he wants her in his life, in his arms and in his bed but he doesn't want to let her in. Because doing that would mean showing her all the sides of him he is most ashamed of, the ones that resemble Damon so strongly he wants to scream.
It would mean letting her see the monster he keeps chained inside, its thoughts menacing and dripping with blood to the beat of her heart; who's ruby eyes and veiled fangs long to just rip and tear and taste every time she tilts her gorgeous neck up to him while he places seemingly innocent kisses along the pulsatingly naive lines of it.
He wants to keep her safe, but he's selfish enough that he wants her close to him as well, despite that being more dangerous than anything she may encounter wandering the quaint little streets of mystic falls. So he holds her at arm's length, never quite letting her get past that deep, brooding Stefan Salvatore mask while at the same time taking her trust and taking her body and pretending not to see the way his big, evil, bad older brother stares at her- the way he secretly wants to: lust and hunger and possession and love all rolled into his gaze- and the way recently, she's been staring back too.