Kanji are not always read with on/kun readings, there are other readings as well (for example words like 大人 and 今日)
Learn a few words, rather than learning readings out of context. There are some readings which are relatively uncommon (白 as びゃく I think is far less common then the other readings) or are attached only to certain meanings. For example, 日 is never read ジツ when in compounds where it means "Japan"; it will be ニチ , and there are sound changes, so 日系 (person of Japanese descent), is read にっけい not につけい.