Squirrels are highly unlikely to get aggressive for no reason. Keep in mind, however, that these animals have a sharp vision and smell. If they perceive a threat, the squirrels are very likely to get in a fight or flight mode.
A squirrel that’s cornered by a human being or a pet like a cat or a dog is likely to defend itself and bite. Attempting to pick up a squirrel without wearing gloves is a big no-no. It could use either its claws or the sharp incisors to defend itself. Regardless of this fact, squirrel bites aren’t all that common. Of all animal bite cases, only one percent can be attributed to a squirrel bite.
As you can already see, attempting to hand-feed a squirrel is another big mistake. Even if the animal is amicable, it can bite the hand that feeds it (literally!) accidentally. If you have to feed a squirrel from your hand, put a leather glove on and place the nuts or seeds on the horizontal palm.