I have had an XR400(sold), YZ125(for sale), and YZ250F(new) recently and had the same problem as you when I first got the YZ125.
Everybody else seemed to effortlessly start there 2-stokes and I had big problems -- finally figured it out.
As opposed to the manly, full leg stroke that you give the 4 stroke, the 125 requires a quick hard stab. Forget about the leaning over stuff. Use the choke unless it is quite warm outside. Of course you have to give it a little throttle, unlike your thumper.
Most importantly -- check the plug if it doesn't start after multiple kicks. My 125 sometimes would start briefly, but wouldn't "clear out" and had fouled the plug. Other times it hadn't turned over at all, the plug was wet (from all the kicking). Replacing the plug at this point always worked. The problem was greatly improved with a leaner pilot jet.
Good luck, and enjoy the ease of starting once it's warmed up and you stall or crash.