Yes, man is fashioned to attain life ever after in Jesus Christ, Who is the light and life of men. Yes, he has a beginning and therefore is not eternal, for eternal has no beginning in our understanding, existing from everlasting to everlasting, as it were, which applies only to God.
But the question was more one addressing the notion that man's soul cannot die, as if God is powerless to extinguish it from His creation, even though Scripture explicitly states that God can destroy the soul. Jesus told us to fear the One Who can destroy both body and soul. People often speak as if the soul cannot die no matter what, in fact they say it is immortal, even though Scripture explicitly says only God is immortal; they say it even while admitting that when the body is dead, the soul lives on as if it were not tied to the body, which means they are overlooking the fact that man became a living soul when the breath of life entered the physical elements of man.