when a believer says there is evidence and the atheist says “that’s not evidence” that is just the atheist’s personal opinion. It does not mean it is not evidence just because it did not cause that atheist to believe.
The proper interpretation of evidence is not as subjective as you suggest. Reason is not whatever one wants it to be. Reason is the rigorous path between premises and evidence to sound conclusions. There is only one proper method of doing this. I have offered the example of applying reason (the rules of addition) to a group of numbers to be added. There is only one correct answer.
As the definition says evidence is “anything that you see, experience, read, or are told that causes you to believe that something is true or has really happened. “
Yes, evidence is that which is evident to the senses. That's all that the word means until one adds the preposition "of" - evidence of what?
I would quibble with the idea that whatever a person sites as the reason for their belief constitutes evidence for that belief. People misinterpret evidence continually. Look at what people offer as evidence for a god. Some offer scripture. The words say there is a god. Not evidence of a god. Some offer the world around us and its beauty and complexity as evidence of a god. They are also wrong. The universe is evidence, but of what, apart from it being there? To say that it is evidence that supports a supernatural explanation over a naturalistic one for its existence is simply wrong.
Who defines what valid reasoning is? What is valid to one person might not be valid to another person as people all reason differently and two different ways of reasoning can both be valid.
Once again, the matter is not as subjective as you suggest. Valid reasoning is that which, because it is fallacy-free, leads from evidence to sound conclusions. Conclusions are not called sound because they follow that path, but because following that path is the only known method for arriving at conclusions that can be demonstrated to be correct. I refer you once again to the example of reason (the rules of arithmetic) applied to a column of numbers. Somebody who can't add properly might reject the consensus of men and machines that add meticulously all coming to the same conclusion (sum), and say, "Well, that's not how I choose to add those numbers, those aren't my rules. Who is to say that your rules of addition are the only proper way to combine addends?"
Incidentally, valid in the discussion of reason means correctly reasoned without fallacy, and leading to conclusions that are demonstrably correct. There aren't two paths or two conclusions that are equally valid. There may be two choices such as the naturalistic and the supernaturalistic, and reason might not be able to rule one out or the other in, but that doesn't mean that there are two valid conclusions. There is still only one. The valid conclusion is that both ideas remain possible. Other opinions, such as that the supernaturalistic one is correct, are simply fallacious reason, and the conclusion that one of these is correct is a non sequitur, that is, a fallacious conclusion not adequately supported by what has come before.
The other problem is when people think that they know how another person arrived at their belief when they don’t know the half of it.
I get that from the antivaxxers as well. They think that we don't know what evidence they evaluated or how they came to their present position to refuse the vaccine, and so shouldn't challenge the validity of their reasoning or the soundness of their conclusions. But they are also apparently unaware that skilled critical thinkers can do exactly that. It is glaringly apparent to such people that those refusing vaccines are not going from evidence to sound conclusion. We hear their arguments. We see what evidence they claim supports them, and we reject their reasoning, because their conclusions are not derived from any prior evidence or valid reasoning applied to it.
So yes, it is very possible to conclude that somebody else's reasoning and conclusions are invalid. I think that you might not be aware of that given your implied claim that without knowing exactly how they arrived at their conclusions, we can't call them unsound.
Look at how many people come onto RF and star threads with arguments that they call proof that a god exists or that evolution is wrong or whatever, and then present arguments that are easily dismissed. They become indignant that such ideas are rejected. They tell us that we are indoctrinated and need to learn to think outside the box or be less demanding regarding the rigorous evaluation of evidence. The tell us that they are certain of their conclusions, as if that would make them more valid. They have a better way of thinking, more open-minded, and we are pig-headed to reject their conclusions. If they're talking about some condemnation of evolution, they lament that their papers are rejected by the referees of credible scientific journals.
But we reject their claims nevertheless base on their merit. If their so-called proof doesn't convince anybody, it fails to be a proof, even if they call it that.
Who is a skilled critical thinker, is there a college degree one gets for that? No, there isn’t. Some people just ‘believe’ they are skilled, more skilled than someone else. I consider that arrogant.
No, there is no degree in critical thinking, although those who learn to do it properly generally learned while acquiring an academic degree.
And you may consider it arrogant that critical thinkers can recognize one another and agree about what constitutes sound reasoning, but it is simply a fact, just as they can recognize those who can add properly. Saying that the group that uses the rules of arithmetic properly to come to the same sum which can be demonstrated to be correct empirically if needed (one can show that 67+112+678=857 by combining 67 apples with 112 more and 678 more and counting how many one has) - calling these people arrogant for believing that they are more skilled adders than those who can't come to their conclusion is wrong. Calling others incorrect when they are demonstrably so using the techniques of critical analysis to demonstrate that they are incorrect is not arrogance. it is a useful service. It is a gift to humanity.
I imagine that you also think it arrogant to say that there is no rational reason to refuse a vaccine apart from it being medically contraindicated. You might say that nobody can know the reasons that led another to the decision to refuse, or that they interpreted the evidence differently, as if that were just as valid. There is this idea that if people don't reveal their innermost thoughts, one cannot judge the merit of their conclusions, which might be just as valid as those from critical thinkers that reject them
I take you back to the summing of addends. One doesn't need to know what tortured thinking another used to arrive at an incorrect answer, nor to reject the objection that he need to be a little less rigorous in my thinking, or that he is arrogant for calling a wrong answer wrong.
Same with the antivaxxer. A skilled critical thinker can accurately define their position as irrational, that is, not derived from the proper application of valid reasoning to the relevant evidence. It is based either in fear or tribalism, not fact. I know that such people dislike being thought of this way, and several here on RF have pleaded with others not to judge them for their antivax position, but as they have seen, that's just not how it works. Don't the pedophiles say the same thing - don't judge our love of children, you don't understand it, it is just as pure as adult-adult love. Or insurrectionists who want to be judged as patriots because that's how they like to frame their crimes.
We judge them as well, and possibly so do you. And so will the courts, just as the court of popular opinion will judge the antivaxxers.