Coincidentally, I just discovered that I can do this

. It's murder on my fingers now...they ache like h***

.
I think the trick is several things. I don't know if these are 'correct', but they work for me.
a)
DON'T hold the cards in a tight grip. This will just break the corners. The grip should be loose enough that you can see gaps in the packet if you look at the edge (that is, if it's not new).
b) Once you have a couple of cards woven by sawing them, tilt the packets slightly towards each other on the side that they're woven - only very slightly though! This lets the weave 'spread' through the packet.
c) You do have to use the pinkies to support the packets and provide some of the push (at least, I think so

).
d) New cards, or at least non-dog-eared cards are better than that old pack you found under your desk.
Lastly, just keep trying. One day, you'll be playing with a pack of cards and you'll discover you can do a perfect faro!
Kati