Were Jesus And Paul Celibate?

A reader writes:

Hans Kung says that Jesus and Paul remained celibate.  Well, there may be evidence to the contrary.  The gospels show Jesus regularly preaching in the synagogue and rabbinic custom held that in order to do that a rabbi had to be married.  Many scholars have argued that Paul remained celibate but in the authentic Epistle to the Philippians 4:2, Paul asks his yoked-marriage partner (syzygos) to mediate a dispute.  The early theologian Clement of Alexandria maintained that Paul was married and upheld the institution in his Miscellanies Book III.  When Christianity later got on its celibacy kick in late 2nd and 3rd centuries, many of the evidences of marriage were either muted or expunged from the tradition.