The way I would deal with it is probably not the best. It takes a large part of the emotion behind it all out of the picture. But I don't think the onus is really on you at all. It is your body and your life.

Explain using logical scientific reasoning why you are following the diet. You don't even need to mention the word Atkins if you don't want to. I would put the onus back on her and have her explain from a biochemical standpoint how managing insulin levels over time, using dietary fat as a lipolytic aid, getting all kinds of beneficial micronutrients from meat/veggies etc is detrimental. If she can't explain scientifically why it is bad, then where is her argument? In biased studies? In the media bs? I mean come on.

She is using an emotional argument and falling back on ideas of propoganda etc. Take that out of the picture and see if here logical reasoning holds up scientifically!

That is what I would do. Disassociate the argument from Atkins and focus on science. Take the media out of it.