Should student or supervisor be corresponding author for publications based on student research?
"The corresponding author is the one who take the responsibility of a paper". I've never heard this before. For example: http://sciencecareers.sciencemag.org/career_magazine/previous_issues/articles/2010_04_16/caredit.a1000039 says "The corresponding author is the point of contact for editors, readers, and outside researchers who have questions about the contents of the paper. Often, the corresponding author is also the last author, but she or he may be listed first or even in the middle of the author list."

All authors take responsibility for the paper (or should). The point of the corresponding author is who to contact if you want to correspond about the paper. If this were someone who was likely to move institution (because they are finishing, or have finished their study), they are going to be hard to contact, so make it someone who's likely to hang around for a while. I've never seen anyone take any notice of who the corresponding author is.