I would not say should, rather, a women CAN be an Apostle. The one Apostle means "to send" or "one who is sent". There have been man women throughout history that were sent under Jesus' teaching, to preach the gospel in the world.
I say the same. But in my strong's Apostles means men divinely commissioned to represent Christ. I know women Apostle as well, it was just a question that was asked of me. So I decide to put it out here to get some opinions, and doctrine on this. thankd you for your reply
I agree that apostle means to be sent forth and in Luke 10: 1-3 Jesus sent out 72 in pairs as messengers and asked them not to bring their purses. That seems to be he was talking to women.