At what point does the following argument derail for you?

0) I tossed a coin, it lies flat on my desk

1) You have some degree of belief about the statements H:“the coin shows heads” and T:“the coin shows tails”

2) You want to quantify that degree of belief

3) You postulate that you can put a number on your degree of belief about some statement A with the following properties:

3a) p(A) it is between 0 (false) and 1 (true)

3b) p(A or B) = p(A) + p(B) - p(A and B)

3c) p(A and B) = p(A given B) p(B) = p(B given A) p(A)

4) p(H) + p(T) = 1

5) Unless your degree of belief about H is higher than your degree of belief about T

or your degree of belief about T is higher than your degree of belief about H ...

6) ... it follows that p(H) = p(T) = 0.5