Technically, when someone makes a statement like "It's literally raining cats and dogs", one would actually see cats and dogs falling from the sky.
Literally is the opposite of Figuratively. The expression "It's raining cats and dogs" is a figure of speech. It's a metaphor. It's not ACTUALLY raining cats and dogs. When people say that, they mean that it is raining really hard.
That is the REAL definition.
Informally, Literally is used to express the exact opposite. It's used to exaggerate and create emphasis.
I can literally think of a billion examples right now. I literally laugh my ass off when I hear people use it in this sense.
You get the idea. It defies logic.
It's true that I have a heightened sense of sensitivity to the way words are used. But you know what? I'm OK with the use of Literally being used to mean its opposite meaning (figuratively) as long as it's used informally. I like those moments when it's used this way, when I can imagine and smile about what it would look like if someone laughed so hard their ass fell off.