Take a moment and stack two quarters on top of each other. Now push one over sideways a bit.
That illustrates the secret to mounting tires. Since the diameter of the bead is equal to the tire seat diameter, and smaller than the flange height of the rim, there's no way to mount it unless you can shift things over a bit. The key is that the center of the rim is deeper than the tire seat, and by pushing the tire to the center, you can shift it over, pushing the slack to the opposite side making it possible to lift it over the rim.
many disagree with me, but I prefer to work toward the valve, because that allows the opposite side to go to the deepest part of the rim giving me more slack. If you start at the valve, the stem keeps the tire from moving over as far.
BTW- since you'r going back to the shop tomorrow, ask the mechanic to let you watch, and to show you how he does it.
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