Learn English – A phrase/word for a Logical Jump in argument

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I'm looking for a word or phrase to describe the following thought.
While analysing someone else's writing I found that their arguments had some problem.
For example let's say someone argues that a particular house has slippery floor. So all houses all over the world, that has the same floor-tiles are also slippery. So most household accidents all over the globe happens because of this particular brand of floor tiles.

Although the example I mentioned is extreme, but I want to know how should I explain this.
The phrase that comes to my mind is
The writer made some "leaps" in argument But I'm told this might not be right. Is it right?
The writer has "significant discrepancies" also doesn't clearly espress my thought. He has discrepancy that's okay. But what I want to mean is that, he's jumping from a narrow point of argument and drawing conclusion on a much broader scale. So how should I express this?
And Thank you for reeading this.

Best Answer

There are a few terms for logical fallacies that might fit. In general discussion, I'd call it "jumping to conclusions".

hasty generalization

Hasty generalization is an informal fallacy of faulty generalization by reaching an inductive generalization based on insufficient evidence—essentially making a hasty conclusion without considering all of the variables.

faulty generalization

A faulty generalization is a conclusion about all or many instances of a phenomenon that has been reached on the basis of just one or just a few instances of that phenomenon. It is an example of jumping to conclusions.

proof by example

Proof by example (also known as inappropriate generalization) is a logical fallacy whereby one or more examples are claimed as "proof" for a more general statement.

You might also say that anecdotal evidence or cherry picking is being used.

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