And at that time, Russia promised to respect Ukrainian borders - but then violated that promise. The U.S/NATO present no threat to Ukrainian sovereignty or independence, but Russia does.
As others have stated, Ukraine tried to be neutral, but apparently wasn't neutral enough for the big neighbor.
You get punched by that big guy to the east, and he threatens to do it again if you don't toe the line. The big guy on the west offers to help you out a bit, no threats involved. It's not hard to imagine that you might start to look more favorably on the guy on the west side.