There are multiple reasons why your dosa would stick to the pan.
1. Skillet not hot enough
The pan should neither be too hot or cold. To check if the pan is well heated, do this simple test. Sprinkle some water on top. The water should sizzle right away but not too much that it causes lot of steam.
2. Not enough grease
You don't need to add a lot of oil. Just few drops before making a dosa and spread using a half cut onion or even a paper towel. This rule especially holds true for a non stick pan which does not need grease. So make sure to rub the excess off with a paper towel.
3. Batter does not have correct consistency
Dosa batter should be creamy. Too thick and not well ground can also lead to dosa sticking to the pan.
4. Lack of fermentation
A good dosa while cooking develops beautiful little holes. If yours are missing, you know the batter has not fermented well. This also contributes to Dosas sticking to the pan.
5. Kind of Skillet
Though non stick skillet makes for an easier job, I would personally recommend using traditional cast iron tawa/skillet to make the quintessential Dosa. Ideally, you would want to invest one exclusively for dosas. Using the tawa for other foods like rotis etc tends to make it harder to make Dosas. Keep your Tawa seasoned and exclusive for Dosa making.