The best you can do is:
- Gather facts about what you are doing, hopefully backed by scientific studies.
- Gather facts on how your body is improving. Regular physicals or blood work will arm you with how your body is responding to the regimen.
- Ask questions to engage in dialog.
- Don't get dogmatic. Understand that your family is trying to look out for you, so this isn't something that should divide the family. Also there is more than one right answer.
When you are gaining facts, look at both sides of the argument. This will help you gain a better understanding of why things work. One example is an article on how intermittent fasting stacks up against science. Also understand that there are different variations of intermittent fasting, each with their own advantages/disadvantages.
The bottom line is that when you take proper steps toward improving your health, your body will respond in kind. The fact that the eating protocol is helping your acidity issues is great, but do understand it might be more related to better food choices rather than just the timing of your food.
How to disarm negative arguments
The first thing to do is ask, "why do you think this will hurt me?" There may be something more specific than just intermittent fasting at the core of their concerns. There might be something you can improve in your approach to intermittent fasting. When you hear the concern, and you actually do have an answer for it, share the basis of what you are doing and how it's affecting your health. If you don't have an answer for it, then simply answer "I haven't considered that, where can I get more information?" (do your own search on the information, both pro and con trying to find information from people who actually know about nutrition).
You might be able to arrive at a way to address your health concerns and your family's concerns at the same time. For example, if your variant of intermittent fasting is like the Lean Gains protocol, you have an 8 hour eating window which is ample time for 3 meals a day--and you also have requirements for your macro-nutrients which will improve your overall health. This would probably work better for your situation than a 6 days eating, 1 day fast (or worse a 5/2 day split).
Bottom line is find a middle ground that is based on facts that both you and your family can be happy with.