cpu stuck on cooler

Yesterday, I tried removing my cooler to clean it out and also apply new thermal paste but the entire processor came right off with it, fortunately though none of the pins were bent. I tried twisting it and it wouldn’t budge. Tried using a dental floss but I couldn’t get it right between the...

So I just bought a new cooler which is arriving in a few days and I see that some people rip the cpu out of the socket when they take off the stock cooler. What are some precautions I can take to make sure that this doesn't happen to me?