How can a PhD student defend their correct ideas or claims to their supervisor? I am a PhD student who works in theory. Too many times, I have to defend my ideas or claims in front of my supervisor. I have failed to do so in the past and it worries me.
Please note that I am only interested in defending correct ideas, not wrong ones.

Some of the things I have tried are:


Doubt every line which I read.
Try to prove each term clearly in front of him.
Go over the material at least two times.


These kind of things are not working.

My research supervisor has told me that I need to defend my ideas and claims. There have been many times where he asked me to change something about the idea; I did it; and then he asked me why I changed it.

Question: How to defend your correct ideas or claims in front of your supervisor?

Edit : Many times I have tried to defend a wrong idea and there were some times in which I have changed my right idea ( based upon his feedback) and after I changed my idea he told me "your original idea was right, why did you change it?". How to deal with this situation also?
How to defend your correct ideas or claims in front of supervisor?


If your advisor is anything like me, they care much less about right or wrong in these meetings, but they want to hear what your thought process is and which angles you have covered. Suggestions to try something else should not usually be understood as "you did something wrong, do this other thing instead" but more like a probe whether you have also investigated this other angle, and if you have not chosen it, how you justify not doing that.

As such, the central element in "defending" your idea is to, briefly but clearly, outline why you have done what you have done, and not done what you have not done. Proving stuff in front of your advisor should help, as long as you do it correctly and clearly. If it doesn't, you are either not being as clear as you think you are, your advisor isn't competent in your topic, or you have a much deeper problem (e.g., you and your advisor are not on the same page about what problem is to be solved). However, note that even an objectively "correct" approach is not immune to questioning - maybe there are other approaches that are easier, faster, or preferable in some other way? You need to have an argument at the ready for why you have not chosen them.

If looked at in that light, situations where they suggest approach A in the first meeting and then probe you on your usage of A in the second start making more sense - they have not suggested A because of some secret advisor-tech that makes them know the right answer in advance, and telling in the second meeting that they suggested the idea is not a convincing enough reason to go forward with it by itself. Even if they suggested it, you still need to explain why A was better than other approaches.


  Too many times, I have to defend my ideas or claims in front of my supervisor.


Frankly, I can hardly imagine a supervisor who questions your ideas "too much". As long as they are respectful and helpful, questioning your work and suggesting alternatives is pretty much all that good advisors do. It's kind of the job description.