He will not always chide, nor will he keep his anger forever.
Psalm 103:9 reminds us of two important truths: The Lord punishes sin and relents.
God despises sin, and sin kindles his anger. This anger and punishment is not in opposition to his love, but rather it is the opposite side of the same coin. For if I love someone deeply, then I will despise and oppose the one who harms my beloved. Indeed, I will despise anything that harms my beloved.
Sin, in ourselves or in others, is one such harm. Sin is destructive and disordering. Whenever we depart from God’s ways (i.e., sin), we enter a world of chaos and harm. So, of course, in his love, the Lord would come against sin, both in this world generally and in our lives personally. He thus gets appropriately angry, and he chides.
“Chides” is kind of a strange word here because we do not often use the term today. The original Hebrew word, riv, could be understood as “contend” or “come against.” Thus, the Christian Standard Bible translates this verse: “He will not always accuse us…” Or the New American Standard (1995) reads: “He will not always strive with us…”
So sin angers the Lord, and he opposes it and its perpetrators.
But the Lord relents.
He will not always chide or keep his anger forever.
It is not that he gives up or grows indifferent to our sin. It is that he will forgive those who humbly ask, and, as will be seen centuries after the writing of Psalm 103, he will deal with sin finally through the death and resurrection of Jesus.
This relenting happens cosmically, existentially in Christ, but I also think this is a pattern for our daily and weekly lives.
In your Christian journey, you will find that sometimes the Lord comes at pockets of sin in your life in a way that feels very painful. You feel the heat of his displeasure against sin. Like an antiseptic sizzling on germs, so he will burn away infections of sin in your life. When those days come, just remember this verse, too. He will not always chide. It is for a season. So submit to his discipline and await the new day.
The Lord abounds in steadfast love, so wait patiently through times of discipline. Everything will eventually work out to your good.