Why do atheists use pixies, leprechauns and unicorns, things for which there is no evidence, as examples to compare to God?

Not just atheists! "Proof" is subjective. One cannot "prove" a rainbow to a blind man, or spiritual things to someone blind spiritually. This is no criticism of either, of course.

The problem is in your "demonstrably false premise" assertion. Theists certainly believe it is a demonstrably false premise, but then cannot demonstrably prove that. Any rational person can see why the arguments of theists fail. Theists certainly provide evidence, but it is usually evidence of nature or human psychology that they poorly reason to be evidence of a higher intelligence while using ignorance to support that assertion. In terms of agnosticism, it is even more irrational to consider a possibility that has never been established. For example, life on this planet would actually grant the possibility of other life in our universe to be rationally agnostic of since we have not actually discovered any actual other life. There is nothing like this for magical super Beings that defy the natural order and limitations of complexity with their magic. You could literally replace "God" with "magical fairies" and the arguments for theism and agnosticism are equally as valid, meaning they are not.

Because the time to believe something exists is when you have demonstrable evidence that it does.  The time to believe pixies exist is when you have a clear demonstration pixies are real.  And the time to believe Brahma exists is when you see a clear demonstration Brahma is real.  And the time to believe Yahweh exists is when you see a clear demonstration Yahweh is real.  

Using examples like pixies and leprechauns serves two purposes.  First, it highlights the idea Bertrand Russel set out with his teapot analogy.  It isn't incumbent upon anyone who is skeptical to provide evidence of non-existence.  The burden of proof is upon the person making the claim.  And that would be the same of a celestial teapot, a pixie, or a god.  If you say there is a teapot out in space somewhere, it isn't the job of someone who doubts this to map every meter of the cosmos to show it doesn't.  It is the job of the person claiming it is to show this is the case.  This is what is being highlighted in your quote, "For example, if you can claim god exists without presenting any reliably testable evidence to support your claim, then an Atheist can make similar claim(s) about pixies, leprechauns and unicorns."

Second, it highlights the double standard some Christians like to use.  They say we should believe in God because we cannot show they don't exist (but haven't been able to show Odin or pixies don't).  Yet, they say we shouldn't believe in Odin or pixies because we don't have a clear demonstration of them (but don't have a clear demonstration of their particular god).

I'm not sure. Can you disprove the existence of Elves? No? Therefore they exist. That's theist logic. 

1 Tim 6:3-5;Psalms 14:1; Luke 10:21;Rev 4:11. jw.org

Because they're not the brightest bulbs out there.

1. You have no idea what "faith" means if you're babbling on about 'evidence'.

2. There is no evidence for God's existence.

3. Given the huge number of religions, what ARE the odds that you've picked the 'right' one?

Very true. Theists see and hear the evidence; atheists do not. [Jesus] said, "The knowledge of the secrets of the kingdom of God has been given to you, but to others I speak in parables, so that, 'though seeing, they may not see; though hearing, they may not understand.'" (Luke 8:10)

I'm not sure. But I do know for a fact that if pixies, leprechauns and unicorns gave me half the evidence for theirselves as God has given me, I would believe in them also. But I seek God with a whole and sincere heart and He responded.

A lie for Jesus with a "why" in front!

Shame on you...

I thought you had more class...

You demonstrated that there is plenty of evidence that God exists so well as usual.  Thank you!