Well, the "actual", literal, meaning of the flag is that it represents the confederacy during the civil war. That's the meaning they are objecting to. They aren't interpreting it, they're just sticking with the literal meaning. You are arguing that they should accept one particular alternative interpretation about federalism that you support and that they should assume that is what it means.
Turn it around for a minute and maybe you'll see it in a different light. Say that you saw somebody walking around carrying a Nazi flag. You object to it and he tells you that you are misinterpreting it. He tells you that killing Jews was only part of the motive behind the Nazi's launching WWII. Mostly they were motivated by a desire to rid Europe of communists- a motive he supports- so he is carrying it around to symbolize his support for free market capitalism, not to show his support of the genocide of Jewish people. Do you think that would make it acceptable?
Now, like I said before, I really do believe that most southerners that fly the confederate flag honestly do mean to communicate a message other than support for slavery. I actually think it is mostly just flat out "southern pride", not the angle about federalism or slavery. But it isn't entirely different than the Nazi example either. The symbol literally is the symbol of a regime that killed hundreds of thousands of Americans primarily in order to continue a 200 year long holocaust of systematically enslaving, beating, killing, raping and breaking up families because of the color of their skin. Did the confederacy also have some less objectionable, or maybe even laudable, goals? Sure they did. But that absolutely, emphatically, does not excuse what they did. People are well within their rights to be offended by a show of support for such a thing even if that isn't what the person doing it intended to communicate.