The brake arms are not resting equidistant from the rim because the main/mounting bolt for the brake caliper is twisted. Simply pushing the brake arms into position does not work because you are not twisting the mounting bolt back into the correct position for it to hold the brake arms in the correct position.

You need to loosen the brake caliper mounting bolt before you try correcting it's position, loosening the nut or recessed nut on the back of the fork (not barely loose, I mean loose enough that the mounting bolt can turn, and you are not just twisting the parts that are stacked on the mounting bolt. Next, use a "third hand tool" to squeeze the caliper arms down to the rim and center them. While the brake arms are being held down on the rim, tighten the brake caliper mounting bolt without letting it twist out of position. Most brake calipers have a nut or other hex/wrench shaped part on it fixed to the mounting bolt that you can hold with a wrench while you are tightening the mounting nut or recessed nut to hold the brake caliper securely in position.

I recommend replacing diacompe single pivot sidepull brake calipers because they brake poorly. The brake arms flex, and they don't have the mechanical advantage of any Shimano dual pivot brake caliper.