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Micro-video background music recommendation is a complicated task where the matching degree between videos and uploader-selected background music is a major issue. However, the selection of the user-generated content (UGC) is biased caused by knowledge limitations and historical preferences among music of each uploader. In this paper, we propose a Debiased Cross-Modal (DebCM) matching model to alleviate the influence of such selection bias. Specifically, we design a teacher-student network to utilize the matching of segments of music videos, which is professional-generated content (PGC) with specialized music-matching techniques, to better alleviate the bias caused by insufficient knowledge of users. The PGC data is captured by a teacher network to guide the matching of uploader-selected UGC data of the student network by KL-based knowledge transfer. In addition, uploaders' personal preferences of music genres are identified as confounders that spuriously correlate music embeddings and background music selections, resulting in the learned recommender system to over-recommend music from the majority groups. To resolve such confounders in the UGC data of the student network, backdoor adjustment is utilized to deconfound the spurious correlation between music embeddings and prediction scores. We further utilize Monte Carlo (MC) estimator with batch-level average as the approximations to avoid integrating the entire confounder space calculated by the adjustment. Extensive experiments on the TT-150k-genre dataset demonstrate the effectiveness of the proposed method towards the selection bias. The code is publicly available on: \url{https://github.com/jing-1/DebCM}.