I am trying to find the logical basis for why women cannot be Rabbis in most Orthodox communities. Some people seem to pin it on "Tziut" but there doesn't seem to be a clear biblical basis for that concept. Others point to the general distinction between men and women in Gen 2, but that also doesn't explain anything. Can anyone help point me for places to start?
You could start with the Rambam (Hil. Melachim 1:5) which is based on a Mishna:
אֵין מַעֲמִידִין אִשָּׁה בְּמַלְכוּת שֶׁנֶּאֱמַר (דברים יז טו) "עָלֶיךָ מֶלֶךְ" וְלֹא מַלְכָּה. וְכֵן כָּל מְשִׂימוֹת שֶׁבְּיִשְׂרָאֵל אֵין מְמַנִּים בָּהֶם אֶלָּא אִישׁ:
A woman may not be appointed queen, as it says, “upon yourselves a king” (Deut. 17:15) - a “king” and not a “queen”. A woman may not be appointed to any Public Position in Israel. Only may a man.
You can find a lot of interesting source material in Hebrew at this link.
(No responsibility for the validity of the site or the material; the onus is on you to check the primary sources.)