Dialectic algorithm - For calculating if an argument is sustained or refuted

Also, coming up with arguments where there are none is pretty difficult

That sounds to me like you have never spoken with people who are skilled at debate. It might be difficult for the average person but there are plenty of people who can debate well and argue nearly any point.

But how would you call it?

The first step would be to research whether there is prior art. "Refutation tree" might be a description that gives a better impression of what it does.

"a discourse between two or more people holding different points of view about a subject but wishing to establish the truth through reasoned arguments" which quite fits the function of the algorithm.

The algorithm doesn't care whether or not the arguments are "reasoned" it cares about whether they have counterarguments.

It's also not clear that the statements have a truth value to begin with. Appeals about what should be done, are value judgments. The example claims are also ill-defined. It starts with the question of whether everybody should be vegan and later people make arguments based on them defending that people should eat little meat. Motte-and-bailey is in full effect.