Perhaps you're thinking of a video game, because I'm sure that what you posit makes no sense whatsoever in hand-to-hand combat.
A shield is just movable armor. It's big enough not to require a lot of accuracy in placement, just a shift toward the direction of attack. Its design, at some minimal level, will resist blows from hand weapons passively, i.e. requiring no strength. You could faint underneath a scutum and it would still deflect the odd sword thrust from your body.
Even if you're 100% successful in blocking his blows with your shield for the first few minutes, however, you'll eventually get tired, and find yourself on the pointy end of his blade. If you don't run away, you must attack him and kill, injure, or frighten him enough to remove that threat, and the enemy is not going to impale himself on your sword in the spirit of cooperation and fair play. Stabbing, slashing, or punching a disabling blow is going to take a lot of strength, and if any civilization used its dominant arm for shielding instead of swording, it's not likely to have lasted long enough to have a written history.