Great question and thanks for raising. And this one is actually difficult and takes time & practice to improve.
In real life, the way you overcome this is by preparing well when you can before that client meeting, deliverable submission or presentation. You practice, anticipate questions and prepare your evidence. One important shift is that a lot of such discussions are now moving to collaboration & co-creation i.e. its not a one way traffic anymore- consultant -> clients. Both parties debate, discuss, collaborate & co-create an approach/solution together.
But, in case study interviews you dont have the luxury of "preparation time" on the spot. One way would be to be holistic when you are asking your clarifying questions, preparing the framework and making your hypothesis. Take extra 30 seconds to ask yourself- "what else inside or outside the company am I missing". Be mindful of any attributes/areas you have ignored and have an answer ready to defend it. When the interviewer challenges you on a particular point, accept the challenge but dont change course straightaway. Ask for a few seconds to check your work before you tell them you are going to accept/reject their suggestion. Defend your approach if you can or course correct if you genuinly made a mistake or missed something. Same thing applies for market estimation questions.
It is not easy and will require practice.