It all seems based on Paul saying it was better not to be married.
It is a Catholic church rule, not even doctrine or dogma.
Most likely, priesthood in Middle ages was such a high level in the social order, with high material rewards in security and material comfort, that there was very stiff competition to be a priest.
This would be one way to trim down the competition.
It predates the Christ and goes back to Judaism.
The Temple Priest were required to be celibate on the days that they performed sacrifices in the temple. It was part of the rituals of purification prior to performing sacrifices.
The priest could be married but must be celibate on the days of sacrifice. But the priest rotated the duties of performing sacrifices, so they needed only be celibate occasionally.
Also, sacrifices could only be offered in the temple in Jerusalem so a priest anywhere else was not obligated.
Roman Catholic priest are required to offer the sacrifice of the mass daily, so such an arrangement is impossible.