There's are widespread styles of teaching "mathy" subjects that completely ignore mathematical rigor (which is fine).

Often a way to do this (which I personally dislike, but it's also objectively "fine" teaching and can be done very well) relies on "manipulation of symbols" rather than "manipulation of mathematical objects". This is a bit like like learning programming in a language that has macros but no functions. Usually, this includes teaching a set of rules ("allowed manipulations") that allows proving a contradiction, the remedy being that you just don't, perhaps by relying on your "intuition" and knowledge of the problem domain (as opposed to just the math), which only comes with experience and isn't taught systematically.

The style of teaching that I find just intolerable pretends to be doing formal math, keeps telling you that rigor is important, floods you with definitions and terms, and then just does the "macro style of math" anyway, while skipping rigorous theorem statements (let alone proofs) entirely. Unfortunately, I find this article comes pretty close to this style.