It's not your email address, it's Verizon's. You are merely the user, based on the relationship with them as your service provider (internet access, mail, etc.).

As one of the other posters indicated they have a service tier that doesn't include providing ISP services. The problem is that most call center reps don't know about it because they focus on (are graded on) how many upsells to the highest tiers they have.

But for $20 a year (or whatever), they will - if you can find the right rep - just let you be a mail customer and continue to provide you that email address.