Strangely, the first part of your reply would be more damaging to your own case than to mine.
"Everything that exists requires an explanation of its existence" is an axiom if I've ever heard one.
You admit that all physical things require explanations of their existences, but not metaphysical things. Rather than attempting to refute this, I'll use it against you.
This would mean that the Big Bang (physical) requires an explanation, but God (metaphysical) does not. And if God doesn't require an explanation, then what use is it to ask what his explanation is, as if that refutes him?
How do you know when something is self-existent? I don't see an explanation for that.
The very point of my argument was to demonstrate the existence of a self-existent being.
Can you explain "exists in it's own necessity"?
n. 1. Inherent existence; existence possessed by virtue of a being's own nature, and independent of any other being or cause; - an attribute peculiar to God. (source)
Eternity is not defined through time, necessarily. I usually use the term in reference to that which "was" before time and that which might be "after" time—it is that which transcends time. Time cannot be self-existent, because it is not eternal. If a thing existed of the necessity of its nature, it would always exist. But time had a beginning (see here).
If you were suggesting time be the First Cause, I'd respond that time can't cause anything of itself.
...why can't the Big Bang be self-existing?
Because it had a beginning and an end. It wasn't eternal. If it were necessary, it would exist even now. It doesn't.
My argument stands.