Hi everybody,
Summary:
after a lot of manual editing, I finally can confirm what some users already wrote, namely that removing the entries "son", "daughter", etc. ... solves the issue. Now my contacts are syncing correctly again between my MacBook and my iPhone.
Explanations:
I removed the entries "son", "daughter", etc. ... on my MacBook. Even after doing that the syncronisation still did not work properly till I realised that (!!!) the entry "mother" was set as a standard field in the template for vCards: "contacts --> settings". Removing that standard field from the template made the syncronisation possible.
Why do I write this in such a detailed way? I want to emphasise that it is not sufficient to remove all entries "son", "daughter", etc. ... from your contacts. Additionally, you need to remove those fields from standard template in the application "contacts", too. As far as I know, you can only edit this template in macOS, but not in iOS - or at least I could not find it on my iPhone ("settings --> contacts"). I do not know whether you can edit the template in iPadOS as I do not have an iPad.
Final thoughts:
Eventually, I would like to ask Apple why they do not remove those entries completely if it is obvious that these entries make the syncronisation fail? So many people here have reported it and this bug should have reached you, Apple.
Good luck to you all with editing your contacts and making the sync work again!