In the sentence "I can't cook very well but I can make a good omelette," both parts before and after "but" are main clauses.

clauses 是 clause 的复数形式，clause 是语法术语，指"从句"或"分句"。 在语法中，main clause 指"主句"，即能够独立表达完整意思的句子部分，不需要依附其他句子成分。