The NT writers quote the OT hundreds of times, yet they never once quote from the Book of Ecclesiastes. Doesn’t this indicate that the NT writers did not consider the book to be inspired by God?

Norm Geisler and Tom Howe answer this question in their book, When Critics Ask: A Popular Handbook on Bible Difficulties:

There are several OT books that are not directly quoted in the NT, including Ruth, 1 and 2 Chronicles, Esther, Song of Solomon, and Ecclesiastes. However, all these books were considered inspired by both Judaism and Christianity. Several points should be kept in mind.

First, being quoted in the NT was not a test for the inspiration of an OT book. Rather, the question was whether it was written by a spokesperson accredited by God and accepted by His people. Ecclesiastes meets this test.

Second, while no text of Ecclesiastes is cited as such in the NT, many of its truths are. For example:

‘What we sow we reap’ (Ecc. 11:1, cf. Gal 6:7)

‘Avoid lust of youth’ (Ecc. 11:10, cf. 2 Tim. 2:22)

‘Death is divinely appointed’ (Ecc. 3:2, cf. Heb. 9:2)

‘Love of money is evil’ (Ecc. 5:10, cf. 1 Tim. 6:10)

‘Don’t be wordy in prayer’ (Ecc. 5:2, cf. Matt. 6:7)

Third, the NT writers had no occasion to quote from every book in the OT. Few Christians have quoted recently from 1 Kings, yet the NT did (Rom. 11:4). Indeed, few believers ever cite 2 or 3 John, and yet they are part of the inspired Word of God. Whether, or even how often, a book is quoted does not determine whether it is inspired.