Have you read the reason why woman can not be ordained? I bet you haven’t so why do you assume it is irrational? And you must understand that the ordained priesthood in the Orthodox and Catholic churches is way different from the ordained ministry of Protestant churches. The Protestant churches do not claim or hold to the teaching of an ordained priesthood with the priest being alter Christi. They do not have a sacramental theology.
The Catholic and Orthodox do. So don’t try to see Catholic/Orthodox teaching and beliefs through Protestant glasses. It does not work.
I wish I had a link to an Eastern Orthodox defense of the all male priesthood. Since I bet any Catholic source would earn your automatic contempt. Perhaps an EO freeper would be so kind as to provide one.
The prohibition is more likely to be based on a priesthood made up largely of men who don't enjoy the company of women.