Three possibilities:
– If it rubs only in one point, your rim might be out of true. And if if wobbles more and more, it might be because you have one broken spoke. Pluck all spokes to make sure it's not the case; replace the broken spoke (if it applies) and true the wheel.
– You didn't turn the screw enough. Turn "the screw that adjusts the tension on the spring"; there usually is one on each arm, so release one and tighten the other one. Squeeze the brakes a few times to get rid of any leftover resistance and see what happens. If you can tighten on both sides, it may be better to tighten both screws a bit to increase overall spring tension.
– One or both pivots need grease. That's especially plausible if you ride through winter or other bad conditions. Remove the cable, remove the pivot bolt that holds the arm, then remove the arm.
Clean pivot and hole inside the arm with WD-40 or some other solvent/cleaner. Then put grease on the post, put the arm and put the bolt back in place.