I had a huge mental block to get over before I could do a butterfly...I'll tell you the little progression that helped me to get it.
First do a basic invert. I invert with the pole on my right side, so my right hand is below my left. I drop my right hand down to become my low hand. Left hand stays in the same place on the pole, close to my hips. (If you invert opposite me, just switch all the L/R)
I started doing this with a wide split grip (keep it wide so your body stays close to the pole), but many people find the forearm grip more stable and secure. So try both, also try both sides, you may surprise yourself.
Ok, so get your arms into whichever position you choose and this is where I would get stuck...I could not for the life of me make my leg (the one behind the pole, for me it is my left) let go. I felt like I desperately needed it to stay up. So instead of trying to drop the entire leg back, I kept squeezing at the knees, and began by just trying to bend my left leg at the knee and taking my foot off the pole.
It was just enough to help me realize that I didn't need that leg on the pole. Once I did that a few times, I realized that I could drop the rest of the leg. The thought of it didn't scare me anymore, so I did. I bent at the knee first, then slowly released the knee squeeze and dropped the leg behind me.
Butterfly, tada! I hope it works for you too, Good luck. :)