Just chiming in, if another made a claim that seemed too far fetched I would ask at least what their personal evidence was. I would take it, for what it was, personal evidence. I won't necessarily agree but it would at least be considered.
Perception is individual. One can not convince me to perceive things a certain way, unless I allow it. I make the decision based on my own experience and experience of trustworthy sources. Everyone should do this.
I will be back later to continue our discussion from earlier
As a rule of thumb, I define evidence as something that would be needed to convince me that I am wrong, or cause me to believe in something I currently don't believe in.
If you are frustrated that people are not accepting your evidence as evidence, ask yourself a simple question. If that same evidence were presented by someone else as evidence for a deity you currently don't believe in, would you find it compelling? If not, then you need to work on that evidence.
A good official definition of evidence is "the available body of facts or information indicating whether a belief or proposition is true or valid." Do personal beliefs indicate whether something is true or valid? Not really. Most of us require evidence to be independent of the person making the claim. For example, we wouldn't trust forensic evidence if only the prosecution were allowed to gather and test the evidence. That is why all DNA evidence is required to be made available to the defense for their own independent testing.
We also tend to not consider circular arguments as evidence. This is the problem with many biblical arguments. We are told that the Bible is true because it was written by God, and God can't lie. A claim can't be its own evidence.
So overall, you need to consider how compelling a type of evidence is, and how that evidence is independent of your beliefs and claims. Those are the rough outlines of what makes good evidence.
Added in edit: If you want to "get inside the head" of atheists, Carl Sagan wrote a good essay called "The Dragon in My Garage" that tends to reflect my own view of evidence as it is given for deities. I also get the impression that it is quite popular amongst other atheists as well. Here is a boiled down version written by Sagan:
"A fire-breathing dragon lives in my garage" Suppose (I'm following a group therapy approach by the psychologist Richard Franklin[3]) I seriously make such an assertion to you. Surely you'd want to check it out, see for yourself. There have been innumerable stories of dragons over the centuries, but no real evidence. What an opportunity!
"Show me," you say. I lead you to my garage. You look inside and see a ladder, empty paint cans, an old tricycle--but no dragon.
"Where's the dragon?" you ask.
"Oh, she's right here," I reply, waving vaguely. "I neglected to mention that she's an invisible dragon."
You propose spreading flour on the floor of the garage to capture the dragon's footprints.
"Good idea," I say, "but this dragon floats in the air."
Then you'll use an infrared sensor to detect the invisible fire.
"Good idea, but the invisible fire is also heatless."
You'll spray-paint the dragon and make her visible.
"Good idea, but she's an incorporeal dragon and the paint won't stick." And so on. I counter every physical test you propose with a special explanation of why it won't work.
Now, what's the difference between an invisible, incorporeal, floating dragon who spits heatless fire and no dragon at all? If there's no way to disprove my contention, no conceivable experiment that would count against it, what does it mean to say that my dragon exists? Your inability to invalidate my hypothesis is not at all the same thing as proving it true. Claims that cannot be tested, assertions immune to disproof are veridically worthless, whatever value they may have in inspiring us or in exciting our sense of wonder. What I'm asking you to do comes down to believing, in the absence of evidence, on my say-so.
The Dragon in My Garage - RationalWiki