The issue as I see it is that the probability exists that the other envelope contains Z/2 or 2Z, but not both - ie. the probability that one of those exists negates the other from existing, because in order for both to be possible you're introducing a 3rd value where only 2 existed at the start.
So there is 50% probability that the other one contains Z/2 and 50% that it has 2Z. Do you disagree with that statement?
I have two values A and B. I ask you to select one. What is the probability that the remaining value is C? Obviously it's zero.
No it doesn't. According to the problem, both 2Z and Z/2 are possible and you don't have the information to decide either way. Think of a simple coin toss, before I show you the result it is 50-50 to be heads or tails, even though it is just one of the two.