First, this is in the potential form ("to be able to "). You can forget any definitions based on passive ("to be attracted/charmed/distracted/etc").
literally means "to attract". In this context, means "to allow the opponent/attacks to get closer", and that's what you need to do when you try to achieve ("paper-thin margin"). I think here refers to efficient dodging moves (eg swayback), not the overall distance between you and your opponent. If your dodging technique is bad, you have to keep a distance from the opponent and to dodge early and largely, wasting your stamina and losing chances to counterattack. The sentences basically say the boy should correct such inefficient moves.