Yes, women can be, and some nuns are, deaconesses.
Christ chose men only to be His Apostles. He could have chosen women, He did not. We cannot say why this was, but we have not the power to contradict His example. The Fathers do not even consider the idea that women can be priests; it was unthinkable.
Indeed, until secular society in the West adopted the entirely righteous cause of women's rights, not much was heard of it in the Church. The argument that the Holy Spirit is trying to push us towards women priests would be more convincing were it not cast in the language of late twentieth century feminism.
The Eastern Orthodox and the Catholic Churchs take the same view as we do.
It is, of course, not about equality, it is about obedience. After all, not all men can be priests, and not all priests can be bishops; the Orthodox tradition is that only monks can be bishops, which means no married bishops.
Hope that helps, at least until we get a better answer
In this is love, not that we loved God, but that He loved us and sent His Son to be the propitiation for our sins. (1 John 4:10)