You can do better than losing 50%, or you can do worse. Your list members don't necessarily read every email you send. So if you try to do this with a one time email, you may lose more than half.
Most of them are lost in the confirmation process, which is the same place many new subscribers don't get beyond.
So when switching ARs it is best to plan it as a campaign, with incentives to get the subscribers to switch over. A freebie offer with an optin form for the new AR, repeated over time, is one way to do this.
I don't know if logic has anything to do with it. I think information overload, time scarcity, and email deliverability might have more to do with losing people than logic. People respond with emotion, and justify their actions with logic.