You and Byakuya were on a date. it was your third one..he just wanted to make sure you were the right person for him. since..he was normally very picky.

some people never made it past the first date in general with him, let alone the third. so maybe he did want to end up with you.

he took you ice skating. he rented out the whole ice rink, he wasn't going to skate..just wanted to watch you to see what skills you had. if you were 'worthy enough'

you got ice skates and got on the rink, you had ice skated before but wasn't too good.

"Don't fall, Naegi." he said, trying to mask the little concern in his voice.