The scriptures teach:
Joseph Smith Matthew 1:10 And because iniquity shall abound, the love of many shall wax cold;
Whenever a person does evil, he puts himself, to that degree, under the power and influence of the adversary. If he does some small wrong, as is common, the adversary gains only a small amount of power and influence. If he is living in iniquity, he is continually giving adversary great power and influence over himself, and if he continues in such a course he will, at times, act no better than a devil. We see that in the horrific depths of misbehavior wicked men fall into.
We see illustrations of this in the Book of Mormon. We see people whose wickedness has brought them to the point that they are little more than pawns of the adversary. We see the people of Ammonihah gather the believers and burn their women and children alive, after casting the believing men out of the city. We see them gnashing teeth, and showing all the bitterness of hell toward Alma and Amulek in prison.
These are not rational acts. These are men who have given their lives over the adversary. They are not particularly different than the sort of men who crucified Christ.
Now, don't get me wrong. I am not saying that the adversary can FORCE any man to do anything. The adversary cannot force a man to do something. But as he gains greater influence over a man, the power of his temptations increase, his whispers sound so much more compelling.
Frankly, all of us have probably experienced strong temptations at some time, particularly when we are in the habit of misbehaving in some area of our life. We have all probably at one point or another felt strongly tempted to do something we knew was wrong. Satan cannot force our hand. But sometimes a temptation may be particularly compelling.
And the point is the more we yield to him, in rebellion to the commandments of God, the more he has power to influence. It isn't power to force. But he can distort the way we see the world. He can inspire wicked men to be angered against a good cause, and to rise up in support of a wicked one. He can make it appear, to those who follow him, that good is evil, and that evil is good.
He cannot force anyone. But he can exercise great influence on those who yield themselves to him.
Christ said it this way:
John 8:34 Jesus answered them, Verily, verily, I say unto you, Whosoever committeth sin is the servant of sin.
Note that the word verily means "truly" and to repeat it was a way to emphasize it. Christ does that when he is teaching a particularly fundamental truth. The meaning of the truth in this case is precisely what I wrote previously: when we sin, we give the adversary power and influence over us. The more serious the sin, the more serious the power and influence. This is a fundamental fact about our mortal probation.
And realizing that, we can understand the full meaning of the scripture I opened with. It is when iniquity abounds that the love of many waxes cold. Why does their love wax cold? Because their love is stifled and misdirected by the adversary. How can he do that to them? Because they give him power and influence over themselves when they gave way to his temptations instead of yielding to the light of Christ and God's commandments. And among the ways he tends to exercise that power is to destroy their natural affections.
We see this illustrated in another scripture:
2 Timothy 3:2 For men shall be lovers of their own selves, covetous, boasters, proud, blasphemers, disobedient to parents, unthankful, unholy,
3 Without natural affection, trucebreakers, false accusers, incontinent, fierce, despisers of those that are good,
Why are they without natural affection? Because their sins put them in the adversary's power, and he exercises that power to misdirect their feelings and affections. It is the same idea as in the scripture "because iniquity shall about the love of many shall wax cold", i.e. it is teaching that the "natural affection" of many shall wax cold because iniquity abounds.