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I think along with positive self-identity, race-based mentor programs allow students of color to keep their identity and culture. For example, many students have traditions at home like Dia de los Muertos traditions with offerings, Dia de la Raza, etc. and having race-based mentoring groups allows them to continue those traditions and not let go of them since some live far from home and practically live in Pomona most of the year.
Also, these mentoring groups can sometimes help first year students have a friend who they can rely on to help them in case they do not always feel close or such with their sponsor groups. A person than they can get to know even before school starts and make first-years have a better transition knowing they have at least one person to talk to. I know from personal experience my mentor was someone I felt comfortable with and who helped me transition and we have become good friends.
Knowing there are such organizations in which there are people like you who can understand can be, as mentioned, a safe space where students can go. Sometimes there are differences between certain races such as economic status, beliefs, etc that maybe only someone of that same race can understand and help with.