Roughly half of the National Parks are focused on history, and the majority of these are east of the continental meridian (and most are relatively small), so if we look at the actual number of parks, there is actually considerable balance. The impression is that there are more in the West because of the overwhelming amount of acreage included in western "nature" parks. The history about how the western parks developed is addressed by /u/bookwench.

Western half had less inhabited land than the easternhalf when the national parks system was implemented. Also, western US has some spots nobody sane should ever develop,no matter how pretty they are.... Yellowstone. Best way to handle that mess is to turn it into something nobody can build anything stupid on, like a chemical plant or nuclear dump...

Edit: sorry, I missed which sub this was.

More mature response:

The timing of the creation of the national parks system, and the timing of the expansion of Western expansion by industry and development, meant that the western portion of the US has more properly unspoiled wilderness to be turned into parkland. It's difficult to turn already-populated land into a park, and the eastern US was already well-oiled with farms, cities, and people.

And some portions of the park system in the West take advantage of unique features of that land which make is unsafe for other purposes. Yellowstone is wildly geologically unstable and some areas leak sulfuric acid or lethal gas. It's better to call it a park so nobody does anything else with it that could actually be dangerous.