What are the benefits of students studying contemporary art?

Studying contemporary art allows students to broaden their understanding of themselves, their community, and the world. Contemporary art challenges students to grapple with the unfamiliar and asks them to understand that, for many issues, there is no one right answer. It helps them become critical thinkers as they consider the influences that led to the creation of each work of art, such as sociopolitical climate, the artist's training, and cultural influence. Students may be confronted with work that they find unattractive, boring, or confusing, and studying those works of art helps students gain a deeper understanding of the definition of art, and how to discern subjective observations from objective ones. A key point of studying contemporary art is the expanding of the self, as students step into the worlds of the artists and of the subjects they portray, in an effort to understand what it's like to be someone other than yourself.

As the previous educator mentioned, "benefits" are subjective. There are some who say that studying art is a waste of time and that students benefit more by focusing on more "practical" subjects, such as science, technology, engineering, and math, otherwise known as the STEM fields.
What these detractors do not realize is that the study of the arts, particularly visual art, is very helpful in teaching young people new ways of seeing their worlds. Visual artists, such as painters and photographers, encourage us to see those aspects of life that we might take for granted or not otherwise notice. 
Art can inspire imaginative exploration, which can expand into other areas, such as technological innovation. The study of the arts encourages us to "think outside of the box," or to see other possibilities beyond what we already know.
Subjects in contemporary art tend to deal with themes in contemporary life or with the subjects that interest us now. It also applies versatile techniques that encourage us to think beyond our traditional understanding of what art can be. Contemporary art includes not only painting and photography, but also a lot of conceptual art, such as textual art (e.g., Jenny Holzer, Lawrence Weiner). It also allows for the use of non-traditional materials, such as recycled trash.
Finally, the study of contemporary art, along with the other humanities, is key in teaching students empathy. Art allows us to "see" through another person's eyes, which gives us access to an experience we might not otherwise have. The ability to empathize is fundamental to a cohesive society.

It really depends on what students and what you consider benefits. The benefits for elementary school students and for students in MFA programs in the arts would be quite different.
For younger students, visiting studios of artists or museums of contemporary art or having artists visit the classroom helps them understand that art isn't something that just exists in a vacuum but something created by real people. It may give them a sense of the possibility of their creating art as a genuine vocation rather than just as an assignment.
For more advanced students who are studying the arts, visiting galleries and studios helps them understand current trends and make informed choices about their own work and how it is situated in their discipline.
Another issue is that all students are voters or potential voters whose decisions will influence government funding for the arts. Increased knowledge of the works of living artists and the processes of making arts will help students become more informed voters.