The same piece of evidence can both support or refute a theory depending on the explanation we use to judge that evidence. David Deutsch explains this in his book The Beginning of Infinity (ch. 7, in the context of the Turing test), and I'd like to expand on it and give an example.

I recently posted this video of a dog trying to swim when held above water. It can serve as evidence of both the theory that animals are intelligent as well as that they aren't.

If as criterion for intelligence we use the presence of (at least somewhat) sophisticated knowledge, we can say (as most would): that dog is 'clearly' intelligent. He hears or sees running water, he knows he's not touching the ground, and so he tries to swim! Look how smart he is. So cute.

On the other hand, if we understand that any behavior that may just as well have been preprogrammed by the dog's genes and need only be executed mindlessly in robot fashion, then no amount of preprogrammed sophisticated behavior is evidence of intelligence. For example, our computers contain lots of highly sophisticated knowledge, but none of them are intelligent (yet!). So in light of this explanation, the dog is 'clearly' not intelligent.

I put 'clearly' in square quotes both times because, as the conflicting explanations show, one's interpretation of the same evidence can change drastically depending on the explanation we use to interpret the evidence. If things were obvious, that wouldn't be the case, and we should always come to the same conclusion, no matter what explanation we use. We'd all agree with each other.

When people disagree about what a piece of evidence means, it means they use conflicting explanations to interpret and evaluate it. They will not make progress if they accuse each other of not seeing what is plain to see. They need to resolve the conflict between the explanations. If they manage that, they might both learn something new.

EDIT: When somebody describes something as 'obvious', he describes not the nature of the evidence, but the sensation he has when invoking his existing explanation to interpret the evidence, which is effortless. He's being subjective, not objective. He's not being critical, which takes effort. He thereby favors existing knowledge over future knowledge, which promotes staticity and is the hallmark of a static mind.

EDIT 2022-01-02: Slight changes to wording around the video of 'swimming' dogs and linked to video instead of embedding it.