There are those who say that a God of love cannot be a God of wrath. Love and wrath cannot exist in the same God. But why not? "God is love." But what is the opposite of love? "Hate." No! The opposite of love is indifference. If God is angry about something then He is certainly not indifferent. I contend that it is perfectly consistent for love and hate to exist in the same divine Being. Why not? If I love my children I will hate anything that might cause them harm. If I love my congregation I will hate false doctrine. If a shepherd loves sheep he must hate wolves.
The word "kindness" translates the Greek word chrastotas. It derives from a base word which means "to provide what is needed." It is a godly concern acted out. It can also mean, interestingly enough, "to graze." The word "severity" translates the Greek word apotomos, which literally means "to cut off." It can also be translated "to act decisively (or aggressively)" or, you might say, "to strike preemptively." If I am walking through the woods with my child and I see he is about to step on a snake I will act decisively to snatch my child from harm and probably take a preemptive strike at the snake (I don't like snakes)!
God acts kindly toward us. His kindness is His love acted out. He provides what we need. He is our Shepherd who "makes us lie down in green pastures" and "leads us beside the still waters" (Psalm 23:2). But this is also the same God who will act decisively against those who disobey His will. "He who is often rebuked, and stiffens his neck, will suddenly be cut off without remedy" (Proverbs 29:1).
Our God is not a vanilla-flavored God who smiles and looks the other way when we sin. Our sins were paid for at the cross, but there will still be consequences. And those who reject His grace will suffer His wrath--and this is perfectly consistent with His nature.