The general case
The commonly accepted protocol on SE sites is: the author of a post has the final say in edits. So if the author does not want that info there, don't put it there or edit-war with them to force it to be there.
There are exceptions to this, such as when a question's author is resisting badly needed clean-up, but such cases should probably be handled and enforced by a mod. This is not one of those situations.
This specific case
It's pretty reasonable for that author to reject your edit. You should have posted your own answer instead.
In your view, you're just adding helpful information, sure. And it is helpful information.
But in both revisions you're replacing the entire answer with a completely different one! That is not what editing is for. If this were an edit in the suggested edit queue, I'd reject it for this reason:
This edit changes too much in the original post; the original meaning or intent of the post would be lost.
If you want to completely rewrite someone's answer into your own answer, just post your own answer. There is no reason not to. This is still the case even if it's the accepted answer, which should have no bearing on whether you edit or post your own answer. Your edits in this case are bordering on vandalism, except that it's the good variety of completely destroying someone else's answer. (But you're still completely destroying someone else's answer.)
In less major cases, if you want to add substantial amounts of information and they reject it, just post your own answer.