This is not a clear-cut case at all. It's the adviser's job to offer the student guidance, and this includes guidance on whether a particular topic is or is not important, interesting, or likely to get published. Your adviser gave you this kind of guidance. It was negative, you disagreed with it, and it probably offended you. Nevertheless it was a substantive comment on the direction your work was taking. It seems to me that it would be very, very difficult to say that your adviser's comments had no effect on your subsequent work. You probably had them in the back of your mind, and when you wrote up your results as a paper, you probably worked extra hard to write an introduction that would convince the reader that your results were important, interesting, and well motivated. This would be a positive result of your adviser's negative comments.
Does this level of participation from your adviser make it appropriate to add him as a co-author? It's hard to say. Different fields have different standards for this, and you haven't said what field you're in. In many fields, the standards for co-authorship are extremely low; if you make any real contribution at all, you qualify.
So to me, it's very unclear who's in the right, and I've only heard your side of the story.
If I were the editor of the journal, and I got a letter from your adviser complaining that he should have been credited as an author, then at best my reaction would be the one described above -- but in addition I might be persuaded by his letter. My basic reaction would be exasperation and a very negative professional impression of you. You're at the stage of your life where you're building your professional reputation. That's more important than any particular piece of work you publish -- and much more important than whether your adviser is listed as second author on that piece of work.
The underlying issue here seems to be that you and your adviser had a very poor relationship. It sounds like you're done with your PhD, and now, rightly or wrongly, you've antagonized him to the point where he is threatening to do something that will seriously harm you professionally. This means that you've burned your bridges with him. You can't safely ask him for a recommendation in the future. This is a very negative outcome, and now you need to focus on moving beyond it and building a positive reputation in your field.