A lot of what people call logic are things like "not expecting a different result from the same behavior" and "not follow an impulse with no relation to reality" but even those are heuristics. Usually good heuristics but not logic.
That can be semi-formal logic if it's stated as a given rule-of-thumb. Most of the time your debate partner(s) will agree with such rules of thumb, barring some odd edge case. If an edge case is allegedly in play for the context, that path is then explored in more detail.
In IT, often rules of thumb will conflict, such as "a stitch in time saves 9" versus "keep it simple" (YAGNI). In such cases I often use labor hours and finance-like decision making techniques, not unlike deciding on insurance: what are the monthly premiums (ongoing costs), how likely is the targeted/prevented event to happen, and what's the cost of not having the prevention or preparation in place. It's not a perfect model, but at least is a numeric framework to discuss with rather then "I feel that...". Probabilities and money (labor hours).
Stubbornness may be a survival trait for a social animal. We humans are flooded with facts and logic contrived to cause us to sacrifice our own self interest in favor of someone else's. I've even read that the game of social manipulation is why we evolved our huge brains.
I was born stubborn, according to my parents. The same people who accuse me of being stubborn are often the ones who are the most vigorously opposed to gathering additional information that they can't predict or control.