One of the advantages to learning Japanese from a private Japanese tutor is that the tutor speaks the language very well. A native Japanese speaker can help individuals learn to speak, read, and write even very obscure words, and the tutor's knowledge of both the language and Japanese culture can help answer any questions that the student of the language may have.
Another advantage of learning Japanese from a private Japanese tutor rather than in a formal school setting is that the tutor's pronunciation is more refined. This allows the student to mimic the way the tutor speaks in order to improve pronunciation and also gives the tutor additional insight into the inaccuracies of the student's pronunciation. The native speaker as tutor is also far less likely to make mistakes when speaking than a non-native teacher, reducing the chances of such mistakes being passed to the student. One-on-one tutoring also allows the student to practice conversations in Japanese more often, which is useful when the student needs to hold fluent conversations in Japanese with others.
Private Japanese tutors are also good for helping students learn Japanese over a longer period of time. This is because the student eventually learns enough of the language that only an individual native tutor is able to answer more advanced questions about the language.