Module: Basic statistics
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Absence of thought is indeed a powerful factor in human affairs, statistically speaking the most powerful, not just in the conduct of the many but in the conduct of all.
- Hannah Arendt
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Yes, this reasoning is fallacious. The reason is that overall life expectancy is calculated from birth; each age is multiplied by the probability of death at that age, and then the results are added together. An infant has a small (but non-zero) probability of dying at each age from zero to 39 years old. On the other hand, a forty-year-old has a zero probability of dying at these ages, and consequently has higher probabilities of living to each age beyond forty. Put another way, the forty-year-old has already survived the risks of childhood and early adulthood, and hence has a higher life expectancy than an infant. The longer you live, the higher your life expectancy.
The reasoning here also ignores any other information that might be relevant to the life expectancy of this particular man and woman. For example, the life expectancy (from birth) of a female smoker will be less than 83 years, but the life expectancy of a female non-smoker will be more than 83 years.