You may also be holding it up in the air stiffly and at a funny angle.
As you practice, you’ll probably find that you can relax your index finger – even let it bend into an “L” shape – without the yarn falling off. You may also be tensioning your yarn too tightly around your other fingers. At this point I don’t wrap the yarn around my fingers at all; I just sort of drape it over the index finger and curl the others around it. (I admit this doesn’t work for very slippery yarn.)
The important thing is to stay with it for a while and find your own unique way to hold the yarn comfortably. And yes, it’s great to know how to knit both ways so you can switch off from time to time.