As I understand the issue, there is a halachic problem with both women and converts holding positions of sararah (i.e. coercive authority). This is clear in the case of a Beis Din: converts could not judge dinei nefashos before the Sanhedrin, and (as I understand it) cannot generally serve as a Dayan on a Beis Din today when he has the power to compel a born Jew to do something. However, as far as I know, there is no issue with a convert obtaining semicha. I even know of at least one Rosh Yeshiva who has granted some semicha. But we do not allow women to attain semicha, and the general justification I have heard is that it is improper for a women to have a position of sararah. Does merely having semicha put one a position of sararah? If so, why do we permit converts to obtain one? If not, then why do we not permit women to obtain one?
Shalom, Thank you for your question. There has been much written in the past few years about women getting smicha – which I am sure you know is a “hot” topic. Rather than rehash what has already been written, let me refer you to a resource page that lists articles on this subject by many major religious organisations- https://www.torahmusings.com/2018/02/resources-womens-ordination/ Blessings.