Men and women are not equal. There I said it. Let me go out on a branch and say a few other "bold" things. Dark and light are not equal; dogs and cats are not equal; hot and cold are not equal; life and death are not equal; wet and dry are not equal; and (this may confuse many people today) truth and falsehood are not equal. How could anyone say that men and women are equal and really mean it? There are a number of ways that men and women are similar (they both normally have two eyes, two arms, one head etc.) but there are numerous ways that they are not similar (chromosomes, body parts, etc.).
What do we mean when we say that something is "equal"? Take math for example. 2 = 2 (at least when I was taught it years ago). I think most would agree with that simple statement. In a more complicated equation we get things like 1 + 1 = 2. Maybe a bit tough, but I think most would agree with that as well. The point is, "equal" things are exactly the same, not just similar. When most people say "men and women are equal" they often mean "equally as good" or "equally as capable". The first statement is nonsensical since some men are good, some men are bad; some women are good, some women are bad. It is like saying "oaks are equally as wooden as aspens" (so what?). The second statement is patently false. Men are not "equally as capable" as women at bearing children. So the idea that they are "equal" has little or no foundation.
Now Scripture does tell us that men and women are both "joint heirs of the grace of life" (cf. 1 Peter 3:7), but in the same verse it calls women the "weaker sex" (the Apostle Peter's words, not mine). So even in that instance it says that men and women are "similar" and "not similar", but it never actually says that they are equal. Yet, we have heard it said so many times that many have come to believe it (even as ridiculous as it is).
This is not in any way an insult on women (or an insult on men for that matter). It is merely stating an obvious fact that modernism (and especially feminism) wants to erase. As much, however, as modernists seek to tell us to believe something which is clearly wrong, you cannot deny that there are many ways that God has intentionally made men and women different (and thus not equal); and I thank Him for those regularly. Women are designed to be able to do things that men cannot do, and men are designed to do things that women cannot do; this is the way our Lord wants it.
It is precisely because we are "wired" differently that God wants us to keep the created order clear. Gender theory is not really an attempt to find one's identity, it is an attack (and a vile one) on the created order. There are many things that women are just better at than men are, and there are many things that men are better at than women are. Let us be honest with ourselves and admit that fact. To refuse to do so only makes it harder for each one of us to be the person God created us to be. It is not an insult to say that someone is naturally better suited to something because of his or her sex any more than it would be an insult to say that someone is naturally better suited to something because of his or her weight, or height, or education level, or hair color, etc.
With that fact in mind, God has chosen that men are the leaders in the Church. Not because men are superior or anything like that, but because it is more what they are wired to do. Certainly women can lead, that is not the question, but is it what God has called them to do? Rather than thinking of it as "women cannot be ordained in the Church", many women (my wife is one of them) prefer to say "women don't have to be ordained in the Church". The reason that they say this is because they recognize that not being ordained means that they are free to do what they are best at. After all, the Blessed Virgin was not ordained, yet she has influenced the Church in ways that Bishops, Priests and Deacons can never do.
This is also true in the home. Men are called as leaders of their households, and we cannot try to erase that any more than people try to erase it in the Church. There are more verses in Scripture than I have room to quote which point out that fact. And just as priests should lead with gentle firmness, never lording it over their flocks, so also should fathers in the home lead with gentle firmness, never lording it over their families. The gentle and loving influence of a mother upon her husband and children is a power that still boggles my mind, and I will never fully understand it -- precisely because it is not what I am wired to do!
So then, once again, men and women are not equal; never were, never will be, and never should try to be. Let us humbly submit to God's order that He gave to us, and work to ensure that our children see good examples of loving fathers, and caring mothers, as well as many other men and women who live out the calling that God has given them. Let us stand firm and resist all the chaotic selfishness that the world is trying to cram into our brains. God's order is always true, good and beautiful.