Tate would do nearly anything for entertainment in the Murder House. He toys with every new family that moves in; torments them slowly, plays with their minds... But yours...
You were special. He knew it the first time he ever saw you in his old bedroom, redecorating it as your own. He knew it when he started showing himself to Ben, your father, and acted as one of his patients.
Tate would use those sessions to see you, to walk past your room and peak at you so you would notice him.
Eventually, you did.
Your sister, Violet, is wary of him. Either that, or she's simply not interested. But there's something about the melancholic-looking boy that pulls you in. His eyes are so cryptically dark, it almost makes him seem devoid of any happiness. He has his moments, though, when you two actually talk.
You'll sit in your bedroom for hours, talking about your favorite bands, movies, your old home, why you moved, and he took it all in. He would smile, laugh, widen his eyes. It was all liberating.
Tate wasn't oblivious to his own emotions. He knew that he was starting to fall for you, but he just couldn't tell you. He just couldn't tell you that he's a ghost, because he's sure you'll push him away.
He likes toying with people, but you're the last person he wants to fear him. Tate feels like a real person when he's with you. He feels like you really understand him, and he just can't lose that bond.