Did any of those disagreements arise over corollaries to what had been presented???
If you start with a false premise, whatever follows is likely to be untrue.
For example if someone says "Mildred, do you like apples?" and I reply "Why yes, yes I do." And then follow with "Well an apple was stolen at work yesterday, and since you freely admit you like apples, you must have stolen it." The false premise leads to fallacious conclusions, in this case "People who like apples, steal apples." It's a false dilemma.
If I challenge the false premise, with for example "I wasn't at work yesterday." Then that should invalidate the accusation. Instead since the desired outcome is to scapegoat me for stealing the apple, some people will subtly change their rationale to try and retrieve their argument.
We are also in "Affirming the Consequent" territory as just because some people that like apples steal apples, doesn't mean that only people who like apples steal apples.
Accuser: "Just because you weren't working yesterday doesn't mean you couldn't have sneaked in and stolen it, and no one would have suspected since you work here!"
To which I reply "Is there any reason to suspect I sneaked in?"
Accuser: "Yes because you like apples."
So we end up in circular logic territory.
Me: "Well I can prove I wasn't at work yesterday."
Accuser "How?"
Me "I was at a job interview."
Accuser "Job interview!? Well that settles it, only someone who wouldn't inform us of a job interview would be so dishonest as to steal an Apple!"
This is just a generic example based on previous experience. The "Apple" is a placeholder for other things. Incidentally in a similar real life example the "Apple" showed up, but not before I was interrogated, apparently found guilty and was summarily told to pay £600 for an "Apple" that was never missing in the first place.
The logical thing to do would have been to apologise, but that didn't happen.