Never believed and have not believed are not the same at all.
I have not eaten cucumbers today. That does mean I have never eaten cucumbers.
I'm very happy to point your huge error here. When you added the word 'today', that becomes the context in a very limited sense.
So, let's fix your faulty example and see how it goes.
"I have not eaten cucumbers." That's how the Bible states those who "have not believed".
Now, given the statement "I have not eaten cucumbers"; can you honestly and with a straight face claim that the statement is TRUE IF you HAD eaten cucumbers on August 5th, 2016?
Of course, you cannot in honesty and with a straight face make that claim.
If you say "I have not eaten cucumbers" without any conditions or modifiers, that MEANS you have NEVER eaten cucumbers.
To deny this is beyond absurd.
To say I have not done something, one would have to specify whether I have not done if for a year or a month or a moment, or whether I have not done it at all, ever.
And that's WHY my claim is correct. The statement "has not believed" does NOT contain any other specification, such as time, date, etc.
And that's the whole point.
I could say "I have not believed in Santa for twenty years." Without specifying a time period, "have not believed" is not the same as "never beleived"
You've done it again. Your "example" specifies a time period.
The Bible DOESN'T. Aren't you even trying to read the verses correctly?
So, back to your second failed example.
Try this one. "I have not believed in Santa".
Now, if you EVER did believe in Santa, is that statement true? Of course NOT.
When there is no specified time element, or any other condition, that means the statement about NOT doing something means NEVER HAS done it.
If you EVER ate cucumbers, you CANNOT say "I have not eaten cucumbers".
If you EVER believed in Santa, you CANNOT say "I have not believed in Santa."
However, if you NEVER believed in Santa, you CAN say, "I have not believed in Santa."
And, if you NEVER ate cucumbers, you CAN say, "I have not eaten cucumbers."
If you don't see the reality of this, I'm afraid there is will be no use in further discussion.
I can hardly believe I'm having to explain all this to someone whose native language I assume is English.
Now, if you really are an immigrant, arriving here in the past few years, and STILL learning English, you'll get a pass.
But NOT otherwise.
There is no excuse for your errors in how to use and understand English.