The priesthood and the married life are incompatible. You can be a good father or a good priest -- but not both. If one attempted both vocations at once, he would end up being lousy at both.
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Yes, the Eastern Rites permit some mixing of the two vocations. But they are wrong. The Roman Rite is SUPERIOR in that it totally forbids marriage among the clergy.
Yeah, that's a huge stretch, Matthew, to declare the Eastern Rites WRONG. Well, not only the Eastern Rites but the Roman / Latin Rite as well for about the first millennium. So for the entire FIRST MILLENNIUM of Church history, the CHURCH was "wrong", not just the Eastern Rites. Unfortunately, that's the kind of thinking that results from the R&R mentality.
We do know from Sacred Scripture (i.e. from the Holy Ghost) that virginity/celibacy are superior to having marital relations, but that does not mean that the priesthood and marriage are incompatible in any way, or otherwise the Church would not have permitted it for over a thousand years, and in fact continue to permit it for the entire history of the Church in the East.
As for not being able to be a good father and a good priest at the same time ...
Highly subjective, can easily vary from case to case (where there can be many lousy celibate priests but good married priests). MAYBE you could argue that, with all things being the same, the celibate priests can do a BETTER job, but not that doing a GOOD job is inherently incompatible with a married state, both as a priest and as a father/husband. Again, to say that such a priest cannot do a GOOD job is a huge overstatement of your case. At best you can say a celibate priest would be able to do a BETTER job.
Again, not only does that vary from case to case, as I've known many celibate priests that really don't seem to care all that much about souls, whereas some married ones do. AND a married priest with children might be in a much better position to help married couples, parents, in knowing in real terms what that might entail, vs. speaking from an ivory tower when they literally have no clue what it's like to be a parent or a husband, speaking in abstract and often condescending terms. I know just for myself that until I had children I had literally NO CLUE what it would be like and what it was like, and then 2, then 3, then 4, then so on. It's a life-changing paradigm shift. See, when you're a parent, and your child is sick in the middle of the night, you just get up and take care of it, and you don't think you're some kind of hero. There are quite a few priests who would do well to have that same attitude toward the faithful and who could learn a lesson about what being a "father" actually means, since that term is derived from fatherhood itself. Too many celibate priests have a condescending arrogant attitude toward the married faithful, and think that the term Father is just some kind of title of authority rather than a vocation of service per Our Lord's
mandatum, where they have the same attitude towards the faithful entrusted to their care as a father would have toward his natural children.
Or, another way to put it, I KNOW that I would have been terrible giving advice to married couples and parents had I been ordained myself without really understanding what's involved or what it takes, giving abstract textbook answers that show I don't really have a clue what I'm talking about and perhaps do more harm than good. I've heard some couples who relayed some advice they received from their celibate priests that was 100% absolutely HORRIBLE advice coming from someone who had NO EARTHLY CLUE what marriage and parenthood were about in practical terms (they could just give you a theological definition). There's probably no harm in having a mix of some married priests and some celibate, where the celibate priests might be BETTER at some things, whereas the married priest might be BETTER at others (e.g. counseling married couples ... which would be the vast majority of the faithful) ... but to say that one cannot be a GOOD priest at all if one's a father, and vice versa, that's just plain wrong, i.e. that marriage/fatherhood is somehow incompatible with Holy Orders, that contradicts the mind of Holy Mother Church for the first millennium of Church history and for all 2,000 years of Eastern Church history.
Very often Fathers have to work long hours and may have to be away from the home for large parts of the day. If a Father is a medical doctor, he too might be called out in the middle of the night for emergencies, depending on his specialty. So is being an ER doctor also incompatible with and inadmissible for a parent? What's really the difference between an ER doctor who might be called out on emergencies and might have to work long hours outside of the home and someone who puts that same dedication that others have to put into their "career" into serving as a priest? I don't see the difference. From the other perspective, so being married is an impediment to holiness? Well, tell that to the Church, who canonized St. Joachim and St. Ann, although I'm sure a lot of Trads consider them "inferior" or "lower tier" saints. Is there some weird assumption here that all married couples are engaged in marital relations in such as way as to be contrary to holiness? Well, those same individuals might fall into impurity as priests also, except without the bond of matrimony, whether with women, or even worse, contrary to nature.