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This is one of the answer choices given in LSAT exam.
The music critic challenges the grounds on which the music professor generalizes from the particular context of rap music to the broader context of musical tradition and individuality.
I don't fully understand this sentence. Does this sentence mean that the professor have his own logical reasons that support him to generalize particular rap music to broader context of music and the music critic is challenging that logical reasons?
grounds noun 4 Factors forming a basis for action or the justification for a belief. ‘there are some grounds for optimism’ - ODO
The thing that the critic challenges is "the grounds". Your interpretation comes close - the critic is challenging the reason(s) (not necessarily logical) that the professor relies on for his/her generalisation.
