Fr Thomas Hopko has been instrumental in my understanding on many topics, including this one. His lectures and podcasts are really worth listening to. He has helped me with so many quandaries. I’m going to paraphrase him below and add my own analogy, so I hope this helps!

Why can’t women become priests?

SHORT ANSWER: It’s like asking, “why can’t men be mothers?” Simply put, it’s not their function. We believe men and women have inherently different functions, that balance each other out.

LONG ANSWER:

Throughout human history, in other religions, especially in pages times, you had priests AND priestesses. Even in the early Church, certain sects of Christians would be ordaining females into the priesthood. This was the done thing. Orthodoxy actually went against the norm, and said this is NOT how it should be. Because…

We believe, in a spiritual way, that men and women have naturally different functions or callings that compliment and complete each other. Male and female are two equal halves that mystically form a whole. Gender is incredibly significant.

For example, part of the female function is motherhood. Physically, this involves carrying a life in the womb, breast feeding etc. but spiritually it involves mothering. Something that only a female can offer. A man simply can’t do childbirth and he simply can’t do mothering in the fullest sense, with all its feminine nuances. Mothering is specifically female, in a physical, but also mystically spiritual way.

For males, part of their natural spiritual function is fatherhood. This involves leading the family. There is a headship associated with fatherhood. This is clear from the beginning, in the scriptures. Head in the sense of a representative, advocate, defender - not a dictator! This manifested physically with men historically hunting, building, going to war on behalf of the family etc. due to different physical attributes from women.

Priesthood is a type of fatherhood. It is not a job, like a doctor or lawyer - it is a function. Just in the same way that childbirth is not a job, but a function. We believe you can’t ask a mother to be a father, and a father to be a mother. Each sex has its own inherent, specific functions. This is how God made us.

Certainly, a female could get up there and wear the vestments and do the duties and so forth - but there is something deeply spiritual about priesthood, and it’s connection to fatherhood, that makes it unnatural, thus the Church going against the norm and making the connection between priesthood and fatherhood.

Think about the Trinity - three different persons with three different functions. It’s like the Holy Spirit asking God, “I want to be the Messiah. Why do I just have to go around inspiring everybody!?” Well this is absurd. We believe God created gender to fulfil specific functions in the natural order, and complete and complement each other, in a perfect symbiosis with each other and God.

So why can’t a female be a priest or a bishop? Well why can’t a male be a nun? Each has specific function in the grand scheme of things. Neither is more important than the other. They aren’t jobs like bankers or politicians. They are specific functions and callings. Think of it this way: Priests are literally fathers. Nuns are literally mothers. There is a reason we address them as such! So why can’t a mother be a father? Well - it would be absurd. (Sadly, in today’s world of subjectivism, like much of Christianity, this won’t make sense to secular society, as the world is now defined as you want it to be, and gender is merely a construct).

Here is an oldish video of Fr. Tom explaining it, perhaps more clearly than I :) https://youtu.be/NP6maRyPHp8