What does Matthew 24:12 mean?

Jesus is describing to the disciples the harsh reality that awaits them after He leaves (John 16:5–7) and before the end of the age when He returns (Revelation 19:11–15). He has said that they will be hated for their association with Him, that they will be persecuted and killed (Matthew 24:9). Many who seem to follow Jesus will fall away due to that pressure and some will even betray the others. False prophets will rise to teach error and lead many people away from the truth of Jesus (Matthew 24:10–11).

Now Jesus adds that one result of this false teaching will be disorder: a rejection of standards of goodness and morality. Those who follow the distorted vision offered by false prophets will abandon truth. They will rebel against virtue or submitting to God. The ultimate result of that self-serving, self-following lawlessness will be the loss of love. The imagery of love becoming "cold" evokes a corpse: not merely unmoving, but dead and lifeless. As humanity falls further away from the teachings of Christ, it will become less loving.

Famously, Jesus taught that God's entire message to humanity hung on two commands of Scripture: to love God with everything one is and to love one's neighbor as one's self (Matthew 22:37–40). It's not surprising that rejection of God's law correlates to a loss of love for God and for others.