You're pulling like I used to until I was recently corrected. You're right, it does initially feel more natural but it isn't as efficient by a long shot.
Drop your hips a bit more, point your ribcage at the floor, push hard and fast off the floor keeping your hip down until the bar is well and truly moving and drag the skin off your legs with the bar. Pull it into you, not up.
FYI pulling like this will feel a bit more like pulling sumo because you'll be a little slower off the floor by pushing off and holding position, but you won't experience that marked slow-down as your reach mid-shin. Instead you'll just feel the weight keep coming up as long as you stay tight and keep pulling.