Regarding why Jesus chose male apostles, I think you have to start with why Jesus chose 12: why 12 people?
The Jews were a people steeped in symbolism. Whereas we Westerners tend to prefer the literal and the syllogistic, the Jewish (and Eastern) mind is much more about story and symbol. So what would 12 men symbolize? What story does the appointment of 12 men tell?
Obviously, the 12 tribes of Israel. Hence, they symbolized the totality of all Israel. But the 12 tribes are the descendants of the 12 sons of Jacob — twelve men. Thus, they also symbolize the 12 men — who are (in the Eastern mind) the 12 tribes.
Now, if the 12 apostles are the 12 sons of Jacob, who would Jesus be? Who was the leader of the 12 sons of Jacob? Well, that makes him symbolic of Jacob, the father of the 12.
And Jacob’s other name is Israel. By selecting 12 male apostles, Jesus was (among many other things) symbolically staking a claim to being Israel — in symbol and also in prophetic fulfillment.
I have written a post, which won’t show up for a while, on the interpretation of Isaiah’s Servant’s Song, and when you read it, this will make better sense. The symbolism matters at several levels.
For example, we are baptized into Jesus, and so we become a part of the true Israel. Jesus is the true Israel and so those who are within him are a part of the true Israel.
This understanding gives us a different understanding of the prophesies and the crucifixion. But that’s all for a later post.
For now, the reason the apostles were all male is that the 12 sons of Jacob were male — and that Jesus had to become Israel, to pay the price for Israel’s sins, to demonstrate the life Israel was and is supposed to lead, and to bring the nations into Israel.