Remember in the first footnote how I said there are 23 Catholic churches within the Catholic Church, all with different traditions?

This is one of the times that matters. Only the Latin Church, the largest of the 23, requires priests to be celibate.

The other 22 Catholic churches, known as the Eastern Churches, allow married men to become priests, but not to advance anymore.

But even this is a bit of an oversimplification because priests in the Latin Church can be married under certain circumstances.

Most notably, former Anglican priests who were married at the time of their conversion to Catholicism are not required to elinquish their wives.

But as with the Eastern churches, their marriage prevents them from rising any higher.