Infants die, therefore they must be sinners. Death--both physical and spiritual--is a result of sin (Romans 5:12; 6:23). Thus, death cannot come upon anyone unless they are guilty of sin. Since infants die, they therefore must be sinners. Someone may point to Christ, who was sinless and yet He died. But He willingly gave up His life, and He did it to conquer the curse of death that we were under. In fact, God imputed to Christ our sins on the cross, and Christ died in punishment of those sins. (Remember, imputation involves your legal standing, not moral character. Christ was not turned into a sinner on the cross--He remained perfectly holy in His nature. He was counted guilty, or blamed, for our sins.)
If humanity is not born in sin, wouldn't we expect there to be some people who have "beaten the odds" and never sinned? If we are born innocent and good, wouldn't you expect there to be at least some people to have continued in this state and be sinless today? I think all of us know that "all have sinned and fallen short of the glory of God" (Romans 6:23). The fact that everybody sins needs some explanation. The best explanation is that we are sinners by nature--we are born that way. Someone might argue that the reason all people sin is because society is sinful, and thus society renders it impossible for anybody to keep themselves entirely pure. But that only pushes the question back one step. How did society get sinful in the first place? If people are born morally good, wouldn't we expect there to have been at least some societies develop which are morally good?