This is an excellent example of where we sometimes read things into a verse, and see support for a bias we have held all along without looking hard at what the verse actually says.

Does this verse say anything about the biological beginning of mankind?  Christ, of course, is the "last Adam," and Adam is described as the "first man."  But if we assert the first half of the verse implies Adam was the first "biological man," we are confronted with the second half of the verse which by no means could be construed to say that Christ was the last biological man.

On the other hand,  if we know with absolute certainty that Christ was not the last of the human race, than the parallel between Adam and Christ is preserved when we likewise understand that Adam was not the first of the human race.  In other words, just as Christ is not identified as the last biological human being in this verse, neither is it mandated that Adam is the first.

Adam was a living soul, but Adam did not bring life to those who were around him.  True life-giving spirit comes to all men from Christ who fulfilled the mission which was intended for Adam.