How can a PhD student defend their correct ideas or claims to their supervisor?
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.