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.
Also, even Orthodox priests (who are generally married before ordination) are supposed to abstain the night before they offer the Holy Mysteries. But in Orthodoxy, the full Liturgy isn't done daily; it's done on Sundays and important holy days. In the Catholic West, the tradition has been to say Mass daily (except for Good Friday), so the priest would have to abstain permanently.