Why did God let Methuselah live so long?

Answer 1

Tradition states that Methusaleh was one of the most righteous persons before the Flood, and the one who passed Adam's teachings on to Noah and whoever else was willing to listen.

The idea of such exceptional longevity "bothers" us only because it seems impossible today. Seeming impossibility, however, is not disproof. Any disproof would have to come from physical evidence, not conjecture or numerology.

Many ancient nations and historians have records of "unnaturally" long lifespans of the ancients:Manetho, Berosus, Mochus, Hestiaeus, Hieronymus the Egyptian, Hesiod, Hecataeus, Hellanicus, Acusilaus, Ephorus and Nicolaus all state that the ancients lived around a thousand years.

Such records are found in the histories of ancient Sumeria, China, Greece, Persia, Vietnam and India. Such widespread agreement can only be because it (like the Creation) is a worldwide tradition based upon more than mere myth.
See also:

Longevity

Reliability of the Hebrew Bible

Answer 2

Christians who take The Bible very literally have offered a variety of attempted explanations for the great ages of early biblical characters like Methuselah, none of them very satisfactory. These vary from pseudo-science to the divine will of God.

For the real reason for his long life in the Bible, it is useful to look at the biblical lifespan for Methuselah in terms of numerology. First of all, the number 17 was important in Genesis genealogies, from Adam all the way down to the legendary Patriarchs. For Methuselah, the formula was simple, reflecting his status as the oldest man: he had his first child at the age of 187, which is 11 X 17, and died at 969, which is 57 X 17.
The statistical chance of the oldest person in the Bible having his first child at an exact multiple of 17 and then of dying at an exact multiple of 17 are somewhat remote, confirming that this part of the story arose out of the spiritual meaning of the number 17, not history. God played no part in this.