My question has two parts:
The first is what sort of methods the church uses to screen out unfit men.
The second is why not have the option of allowing married men to the priesthood as long as they have no minor children.
In one sense, we could do it tomorrow - doctrinally, there is no issue with married men being ordained.
However, there are several reasons why we continue not to. Among them include:
- the priest's heart would be divided between his wife and his flock - whether or not he has minor children, this would be the case (not that that has not prevented the acceptance of married clergy from Protestant denominations into priesthood in the Latin Rite of the Church)
- If we're following the book entirely and maintaining the traditions of the Catholic Church even where married clergy are concerned, the priest would still be required to be continent even if married - that is, no sex. This hasn't been emphasized in the specific cases of married priests and in the more widespread situation of married permanent deacons.
- The married priest lacks the flexibility to minister and pray as he needs to.
- It inhibits the Christological and Ecclesiological symbolism of the priest, and lacks the radical witness to the Kingdom that is particularly necessary in today's society.
- It would make formation very, very difficult, in the sense that the married seminarian would be separate from the rest of the community; likewise, it would require the wife to be breadwinner during the 6 years of studies, in order to provide for a home outside of the seminary.
Others might disagree, particularly our Eastern Catholic/Orthodox brethren, and that's fine. You can find more in Paul VI's encyclical Sacerdotalis Caelibatus; I would suggest reading it if you really want to understand why.