In the novel To Kill a Mockingbird, why is it weird for an animal to behave the way Tim Johnson did given the time of year?

In Chapter 10, Jem and Scout are outside playing with their air rifles when Jem notices Tim Johnson staggering down the middle of the road. After Calpurnia sees the dog, she immediately recognizes that it is "mad." When Calpurnia speaks to Miss Eula May on the telephone, she says,

“I know it’s February, Miss Eula May, but I know a mad dog when I see one. Please ma’am hurry!” (Lee 58).

Clearly, something is odd about an animal with rabies during the cooler months in Alabama. Apparently, rabies tends to be transmitted more often during the summer months when the weather is warmer which is why Eula May questions Calpurnia. Sheriff Tate then arrives on the scene and gives his rifle to Atticus. Atticus reluctantly takes the weapon and shoots Tim Johnson above his left eye. After witnessing his father's expert marksmanship, Jem is in awe of Atticus' abilities. Miss Maudie then explains why Atticus never bragged about the fact that he was the best shot in Maycomb.