Your comment dragged me into a rabbit hole, which is always a welcome surprise.

From my readings, one can always debate whether this reason for celibacy is whole or not (of course, more holy reasons were given, like purity of the ritual among others), but avoiding inheritance from father to sons was certainly a big factor. By barring heirs from the equation, it solved the whole dispute over inheritance. Yet, when it comes to clerical office and priesthood, "property" is not quite right, since it's mostly about usufruct and benefices, moreso. Which can be significant assets, that goes without saying, hence the Church did everything it could, for holy and not-so-holy-reasons, that traditional generational transmission does not apply. No next generation, no problem.

Quite importantly to the Roman Catholic Church, they wanted to avoid dynasties of priests that would grow in importance and out of their control, so they did whatever they could (ban marriage and fatherhood) so that a mis-aligned priest would only be a temporary nuisance to the Institution.

A lot went into this short burst of investigation, like the fact that early Churches were private property of land-owners, building churches for indulgences and power, reinforcing their ties with the Church, and I may dig deeper. Thanks for your comment again, if you have some references you recommend, I'd appreciate you share them!