Sara, sometimes certain rims and tires are a bad combination. I had Michelin Carbons which were horrible with Ritchey rims. Turns out once is notoriously small and the latter is notoriously slightly oversize.

And you aren't really pushing with your thumbs, you really roll the pinched tire away from you over the rim until the bead snaps over. Put the wheel in the crease of your hips as Kalidurga suggests and try rolling the tire away and down over the rim on the far side of the wheel.