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This is not a good way to argue about anything except mathematics. It takes the wrong attitude towards how words work and in practice doesn't even make arguments easier to debug because there are usually implicit premises that are not easy to tease out.
For example, suppose I say "A (a thing that affects X) hasn't changed. B (a thing that affects X) hasn't changed. C (a thing that affects X) hasn't changed. Therefore, X hasn't changed." There's an implicit premise here, namely "A, B, C are the only things that affect X," which is almost certainly false. It is annoyingly easy not to explicitly write down such implicit premises, and trying to argue in this pseudo-logical style encourages that mistake among others.
(In general, I think people who have not studied mathematical logic should stop using the word "logic" entirely, but I suppose that's a pipe dream.)
The word logic is much older than proper mathematical logic. There no real reason to assume that people mean mathematical logic when they say the term.