Verses in question:
Jeremiah 3:12: “Return, faithless Israel, declares the Lord. I will not look on you in anger, for I am merciful, declares the Lord; I will not be angry forever.”
Jeremiah 17:4: “You shall loosen your hand from your heritage that I gave to you, and I will make you serve your enemies in a land that you do not know, for in my anger a fire is kindled that shall burn forever.”
Here the skeptic attempts to pit Jeremiah 3:12 (a promise to Israel that God will not be angry with them forever) and Jeremiah 17:4 (a statement that God’s anger over sin had been kindled and will burn forever) against each other. In Jer. 3 God is calling Israel to repent of their sin and turn back to him and promises that his anger will not burn against them forever if they do. In the second passage God is referring to those who do not turn back to him and how his anger against sin will never end. Thus the contexts reveal that what is being addressed are two totally different situations. One addresses God’s forgiveness of persons, the other God’s holy hatred of sin. They are simply not even talking about the same things and thus cannot be contradictions.
Also worth noting is that “forever” in this case is a hyperbolic statement meant to show the seriousness of the offense.