speakers on yu Torah that Rabbi Herzog and Rabbi kook didn't always agree with Mizrahi there were times where they went with the אגודת ישראל, I don't understand wasn't Rabbi Hertzog and Rabbi kook the head of Mizrahi?

Rav Kook and Rav Herzog were not the heads of Mizrachi, which was and is a pragmatic political party for implementation, and not a rabbinic body of education or halacha. Rav Kook actually made a point of never identifying with any particular party, stressing that the Torah and the rabbinate is for all Am Yisrael, and there’s truth in every ideology. Accordingly, sometimes he sided with the socialists, on other issues with the revisionists, sometimes with Agudat Yisrael, but it's true, most often with the Mizrachi, which tries including it all, "Am Yisrael in Eretz Yisrael, living Torat Yisrael".