Is it an appropriate way for a student to ask for marks? A student requested to meet marker(me) to talk about midterm. He thought the mark was unfair. But we met, he just told me to point out why he was wrong. He got 0 for that question and I had no idea why he thought the mark was wrong. I was unable to give a very clear explanation. And the student just got angry, like I owed him. After this unhappy experience. I decided to let students state why they think the marks are wrong and attach snapshot in emails. If I think the reason is unjustified I will just point it out and refer them to the instructor. Is that a good policy?
Short answer:


  It is expected for an evaluator to give appropriate reasons for the reduction in marks. However, I welcome your new policy -- it portrays openness and trustworthiness. 


Detail:

Evaluation of answer scripts can be a tiresome work and it is only human to make mistakes at times. We usually take extra care when evaluating the final exams, but most would not pay that level of concentration for a mid-term assessment. It is only natural for some students to doubt the marks awarded for some of their answers. In such cases, I believe the students have their right to claim for the marks which might have been overlooked.

When asked why the answer is wrong, it would be the duty of the evaluator to state the reasons clearly. Only then the student can correct the mistake in future. The whole point of assessment tests is not only to measure how much the students have learned but also to set them on the right path and know where they are going wrong. 

The following approach sounds more diplomatic for a student when asking for marks:

"Sir/Ma'am, may I know what is wrong with my answer so that I could give a better answer next time?"

When the evaluator explains the answer, the student can then point to where the explains concepts appear (if they do) on her/his answer. Then, the evaluator can make the necessary correction in the marking.

Politeness is the key. This approach is what I have adopted for my whole life as a student and expect the same for my students too.

Your approach seems quite new yet attractive to me. Usually, clarification with marks are done in office hours outside class. You never really know how this might work until you put this to practice. But it does give the impression to the students that you seem to be a more open and trustworthy evaluator (IMO).