Do you mean refactor or rewrite? If you actually mean rewrite, then get a better plan. Figure out how to proceed with a phased refactor based approach. Fold the refactoring into new features.
Learn to speak in terms that the deciders understand. Speak in terms of FTE hours (cost) and reliability (risk). Speak in terms of What you're doing, not How. When you speak in terms of how, you're just inviting people to micromanage you. They really want to know how many FTE hours doing something is going to take, and how much risk they are exposed to. How you accomplish it is up to you.
If you tell them that next feature will take a year (because you're going to rewrite everything 1st), then they'll probably tell you to take a hike. So, you'll have to figure out how much refactoring you can do with each added feature to still make them happy.
Finally, you can't care more about the problem than the customer (in this case, your employer). You should care about your work, but don't put yourself in the position where you're more emotionally attached than the owner.