Hi Purdy,
What is the main objection specifically? if it is high fat aspect then you can educate yourself about that and that no studys have linked fat and bad heart health definitively. read read read!!!
the nation of sweden has rejected the fat hypothosis and embraced lc,,read up on that it is fascinating. the gov appointed hundred of scientists to look into it and decided low fat was bunk!!!
Tell your family that inuits live almost exclusively on fat and meat. carbs are not an essential nutrient whereas fat and protein are!!
remind them that it is sugar and starch that is the more recent addition to the human diet and so that is why we are all suddenly getting fatter, it is since in increase if sweet convenience/processed carbs.
LC is often recommended for diabetics afterall and diabetics and people who are overweight ultimatly have problem with insulin, the answer - stop your body generating insulin by avoiding sugar/carbs
You say you are doing a very low carb diet but what do you mean? under 50g of carbs per day is considered moderate in lc circles and is usually enough to get to ketosis but is still enough leeway to eat lots of veggies.
under 20g you will be eating hardly any vegetables at all and i wouldnt recommend doing this for very long as you will miss out on vitamins and fibre.
ultimatly if you feel well and are eating a broad range of real food just carry on.
you could always tell them you are doing low GI which is similar (but milder) principles but doesn't have the bad rap LC does. this will cover your selective eating.
honestly i have given up trying to convert my family, the fat=bad is so deeply entrenched. i know that eventually the world will come round and we will be vindicated :)