In the Eastern Orthodox Church, they allow Married men to be ordained as Priest, but Ordained men who are not Married are generally not permitted to Marry. Bishops are also typically unMarried in the Eastern Orthodox Church.
In the Catholic Church of the West, celibacy is a discipline, not a dogma nor a doctrine. Disciplines can change, whereas dogmas cannot. Doctrines can develop, but cannot oppose the original understanding.
So, have we had Married Priests (like St. Peter and others)? Absolutely. Does St. Paul give a great explanation why it is better for our Priests to not be Married? He does.
Are there Married Catholic Priests today? There are. Exception have been made, typically when a High Church Protestant Pastor converts to the Catholic Christian Faith and is already Married, but is asked to be ordained a Catholic Priest.
Here is a great article of a Married Catholic Priest who supports the Church’s teaching on Priestly celibacy.
I will end with this. I work with a Protestant pastor’s Wife and I hear how hard it is to be both a full-time Pastor of a Church and have a full-time job to send two daughters to med-school (both are now Doctors). I honestly don’t know how Pastor “Tom” has the time to work a full-time job, visit people in the Hospital, perform Marriages and Funerals, Attend his children’s Sports events, council Married couples, Family Dinner, prepare his Sunday Sermon, and all the things that being a good Husband, Father, and Pastor of a flock calls them to be. It really is like having two Families.
I listen to a lot of True-Crime Podcasts while I’m working and the ones that get me are men who cheat on their Wife and have another Family secretly on the side! Being a Married Priest would be like this, but only having more than one Family.
We have been blessed with a young Priest and it is sometimes hard to get him to do things with the Knights of Columbus, because he is just “too busy.” And he doesn’t have a Wife on the side.
I get why some believe that allowing Priests to Marry would cut down on the number of Priests who have same-sex attraction (which is a problem in the Church), but there would just be scandals of another type. Bethel Church is going through a big scandal right now. Hillsong New York has had big scandals in recent years. Even in our local area, there have been horrible scandals committed by Married Pastors (and most involving under-age girls). And what happens when this happens is both the Church Family and the Family-Family is severely hurt by this, in addition to the victims themselves who are most harmed by such selfish and unGodly behavior.
We need to be Praying for all Priests and Pastors. And that God will rid our Churches of leaders who are perverting the Faith because of their secret sins.