“Yet in spite of this word you did not believe the Lord your God,”
This is the Word of God without context. Alone it only holds such meaning as the human mind can muster by reason and experience. We might play with the meaning out of context in order to argue with an unbeliever. How the meaning when used in that manner would be heard by the unbeliever without context and fall on deaf ears.
Deuteronomy 1:31-33 English Standard Version (ESV)
31 and in the wilderness, where you have seen how the Lord your God carried you, as a man carries his son, all the way that you went until you came to this place.’ 32 Yet in spite of this word you did not believe the Lord your God, 33 who went before you in the way to seek you out a place to pitch your tents, in fire by night and in the cloud by day, to show you by what way you should go.
In context the unbeliever is reminded that they have in fact seen God move in their life and refused to acknowledge that it was God. Spite in this case is an arrogant disregard of grace. Grace like the manna in the wilderness needs to be gathered or it will fade away like the manna. Eventually grace ignored with arrogant disregard will stop falling.
We might ask rightfully what that has to do with us today.
2 Corinthians 4:15 English Standard Version (ESV)
15 For it is all for your sake, so that as grace extends to more and more people it may increase thanksgiving, to the glory of God.
How will the lost know the grace of God if we do not extend it to them? Grace is given to be shared. Receiving grace and holding it dear to ourselves does not glorify God.