Two: Several times in other parts of the N.T. they mention His family, as known to them, and they spell it out as: his mother, father, brothers, sisters (possibly cousins.) No mention of wife or kids.
Three: When Jesus died, he was concerned about His mother being alone, and entrusts her to his disciple John. If He were married, wouldn't He be concerned about his mother AND WIFE being alone, and needing someone to take them into their home?
Four: if Jesus had kids --- blood lines and genealogies being as intensely important as they were, in those days - wouldn't there at least be some mention, let alone controversy, about whether they would His successors? If course there would be discussion of it --- if he left any descendants. But He didn't, so there wasn't.
I rest my case.
Malachi Martin, who ain't no heretic, is in hot water with the Vatican again over his studies of disputes in the very early church over all the plum jobs going to Christ's various Uncles, Aunts, and the cousins galore. The Church at Ephesus was home to the Virgin Mary (and Diana of Ephesus, items of whose cult slipped easily into Christian practice, and from which many converts were undoubtedly made). She was from a large family, Joe was from a large family, and these relatives of which there was no shortage, were of course among the very first converts ... not to mention apostles and disciples. Since these were all collateral relatives, this helps wily old Malachi Martin evade the old sibling question of "the brothers and sisters of Christ," keeping him off the Pope's major radar.
Malachi Martin has dug up some interesting stuff which purports to show that several generations later, the Greek converts apparently weren't too happy about Greek pastorships and bishoprics going to these folks and complained about it to the Pope in Rome, with whom they were in correspondence over the course of that first two centuries or so. Malachi says the correspondence still exists.
Fascinating.