Squirrels are known for being cute, frisky, intelligent, and curious. (They are also cannibalistic, which is not as well known.) Their curiosity sometimes works to their disadvantage, as they will often watch hunters to see what they are doing. And if they can see the hunter, the hunter may well be able to see them!
I enjoy watching squirrels in the park, and feeding them nuts by hand in campgrounds. In the woods, however, they are game animals. I have always enjoyed the heck out of squirrel hunting, and where I live they are open all year long, so I have done a lot of it.
Shotguns, rifles, and handguns are all used to hunt squirrels. Having used all three to harvest a great many squirrels over the years, I can confidently state that rifles and/or handguns are the sporting way to go.