〜ようが〜まいが means, in English, regardless of if or not. ex; あなたが賛成しようがしまいが、私の意見はかわりません。 (Whether you agree or not, I won't change my opinion. ) 出ようが出まいが, 私は彼に電話する (If he answers the phone or not, I'll call him anyway. " It depends on what the next sentence come.

「出ようが出まいが」＝Just as I was going out (of the door) .... For example，「出ようが出まいが、電話が鳴った」＝Just as I was going out of the door,the telephone rang. “よう”and“まい”is auxiliary word here，mean to conjecture something.出る+よう/まい→出よう/出まい. が...が...means no matter,whether For example:「行こうが行くまいが、わたしのことです」＝（whether I）To go or not is my business.