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If you have a horizontal holster you have a very narrow slot to keep the muzzle pointed away from your body. Lifting your weak arm helps but the first 8-10 inches of travel are 2 inches from your chest until the muzzle is pointed down.

edit: A strong side waist carry is much safer when your attacker is within contact range. The attacker can be fended off using the weak arm with a palm strike to the face while drawing the gun.The gun can be brought on target at waist height. The arc of the muzzle travels from the down position to a forward position. If the attacker hits or grabs your arm the gun is pointed in a relatively safe direction.

Using a shoulder holster with a horizontal hold, the gun is pointed backward toward your body at chest height when it clears the holster. Under the same conditions if the attacker grabs your gun arm, the muzzle can easily be redirected toward your body. Your strong arm gun hand is in a weak position across your chest closer to the attackers reach. Contact anywhere on your arm at that point could direct the gun at yourself.