"Relax, all right? My old man is a television repairman, he's got this ultimate set of tools. I can fix it." If you don't remember your Fast Times at Ridgemont High quotes you're probably not alone. The scene is worth remembering because the context is ridiculous. So it is sometimes with software development. The cost and effort of fixing the existing implementation is sometimes just too great. The changes cut too deep. You're better off throwing out the current stuff and starting from scratch.
In software development you rarely understand your problem domain perfectly, if ever. You learn what your customers want through trial and error. Sometimes your organization has made such poor attempts at delivering the product people want that you can't help but throw away what you've currently got and try again with what you learned from your previous attempt.
Managers usually hate to hear such talk from developers. Developers always want to rewrite things. But in some rare cases they're absolutely right. Refactoring is great if you're even remotely close to what you want to do. But what if your product is built on bad assumptions of epic proportions?
Could CVS have been refactored incrementally to arrive at git? Could Windows have been refactored to create Linux? Could MacOS have been refactored to create OSX? Could Internet Explorer be refactored to create Chrome? When do you come to the realization that what you want, what you need, is so far away from what you have that you can't get there from here? When is the cost of making changes to your current product artificially inflated by the technical debt and faulty abstractions to the extent that it's better to throw it all away?
That's the advantage your competition has. You've shown them your near miss at a great product. If the people in your organization advocating a rewrite were magically transported into a competing startup that was creating a competing product from scratch would you be at all worried? If the answer is "yes" then you should use the advantages you have (those very same people plus a more intimate knowledge of the problem domain and where you went wrong) and do something about it. Plus if something in your product actually proves useful you can copy and refactor it into the new product.
There are certainly risks but the rewards are incredible.