The key to mounting tires is to understand that since the tire's bead diameter is smaller than the rim's outside diameter, it's impossible.

Obviously it isn't, so there's a trick, which is to offset the tire to one side to get it over the rim. What makes that possible is the well at the center of the rim, which is deepest at it's center.

So, you want to move the tire do the center and push the slack to the opposite end. The first mistake you made was to pull the valve down blocking the center, which prevented the tire from moving to the deepest part of the well. The second mistake was in not ending at the valve, so the entire tire, except for the last section can move to the well, giving you the maximum slack to work with.