[anrakushi]

Jammie i think you are confusing 音読み (onyomi) and 訓読み (kunyomi)

音読み is chinese readings and they are used with words of Chinese origin. the in most cases if when the word is a compound (2 or more kanji) then it will be the 音読み.

訓読み is japanese readings and they are use with words of Japanese origin.
Something like 50% of vocabulary in Japanese comes from Chinese.