Definition of cryptographic advantage vs. probability of success
Advantage and success probability are just words. Their meaning is in practice decided by how the speakers of the language use the words. You have observed that people use the terms advantage and probability in this way. One could probably argue that this is confusing or illogical or something like that, but such is language.

About dividing by two: remember, the advantage is just a number, and numbers can be divided by two and compared to other numbers. Sometimes, we are able to prove that one number is larger than the difference of two other numbers.

(As for the equation you mention, I think two terms are "advantages" and one term is a "probability".)