I understand Satan’s claim as an ontological challenge: that he (and other rebels, though really he wouldn’t want any other rebel to be this way ) can be like the Most High, existing on our own. If we rebel against the source of our existence, then apart from the grace of God we’re going to die (Satan included).
Of course, apart from the grace of God we would cease to exist anyway, whether or not we are sinners. So being a sinner doesn’t change this. (Ironically, that’s what Satan would like to believe! ) When we sin, we are the ones doing something that will lead to the total death of non-existence. But God (unless annihilationism is true) keeps His faithfullness to us regardless.
What complicates matters is that we are always faced with a choice of deaths to choose from. We ought to be choosing the death of submission that the Son Himself chooses from all eternity in loyalty to the Father (and by which the Son, in servanthood, creates all not-God reality). Even unfallen angels have to choose this holy death, in cooperation with the Son, or else choose rebellion against God. Ironically, the greatest rebels are seeking to have their own life by not submitting to this holy death along with the Son–but no entity can exist apart from the self-existent One (Who Himself submits to death not only so that we derivative entities can live but so that He Himself can, paradoxically, continue self-existence: God self-begotten eternally acting to surrender to God self-begetting Who eternally acts to generate the Son.)
We have to die even more as sinners than we would otherwise have had to die-into-life in cooperative solidarity with God the Son. And apart from the grace of God, that sinful death would be total non-existence. The choice is still ours, every time we are faced with a choice to sin or not: to act again toward the death of non-existence, or to act with God toward the death that leads to sharing God’s own life. But God’s choices in the matter take precedence: we cannot force God to allow us to achieve non-existence (and it would be impossible for us to have anything more than derivative existence, so neither can He ‘allow’ us to exist freely ‘on our own’.) Neither can we force God not to act toward leading us to choose the death that we ought to have been choosing: dying with Him into life, giving our life (which we are given by God) for the sake of other people.
Just as God Himself eternally does.
So, since I vehemently disagree with Satan, that we cannot not be dying (one way or another), then neither do I fail this challenge.
What I find ironic, though, is that traditional damnationists have a peculiar tendency to agree with Satan themselves, that by sinning we will in fact begin to exist “apart from God”, even if this is in “hell”!
(Some traditional damnationists manage to avoid this by thinking more clearly about what they are saying; and of course annihilationists intrinsically don’t have this problem. Usually. Weirdly enough, in the past year I actually spoke with an avowed annihilationist who, when pressed on his doctrine, began to speculate that we would still continue existing on our own, apart from God, despite having been “annihilated”! But I can’t say I’ve found this to be a usual result among annihilationists.)
So, TV: you might ask your friends whether they believe sinners will eventually continue existing “apart from God”, “totally separated from God”, etc. If so, they’re the ones failing the Gen 3:4 test. My own reply would be otherwise fairly similar to yours, I think.