Yes, God is certainly loving. The most loving Being in the universe, for He is the only One Who would give Himself for avowed enemies. No man was His friend, for no one seeks after Him: “There is none righteous, no, not one: There is none that understandeth, there is none that seeketh after God” (Romans 3:10-11).
Yet by His sheer grace, He offered salvation. Now that is love. But His love has many facets, and like we know, His is not a condoning “love” — the “love” that accepts everything, right and wrong, the “love” whose god is personal happiness (temporal, at that).
No, God’s love is mature and holy. He hates sin with a passion: “The LORD tests the righteous and the wicked, And the one who loves violence His soul hates. Upon the wicked He will rain snares; Fire and brimstone and burning wind will be the portion of their cup. For the LORD is righteous, He loves righteousness; The upright will behold His face” (Psalm 11:5-7).
Thus, God will not tolerate sin. He cannot stand sin, and it is with great pain that He allows Himself to endure the sin of history, it is with grace He allows this. He could have — should have! — obliterated us first chance He got. We disgrace Him constantly: “every imagination of the thoughts of his heart was only evil continually” (Genesis 6:5).
We would never love Him, except by the grace He gave us to open our eyes to the glory that is His. Yet He cannot just let sin slide. And this was love: That He absorbed all our sin on Himself and paid the penalty required of disgracing the God of the universe.
He paid it Himself. The God of Heaven humbled Himself as a man to pay our debt so that we could find true happiness, the happiness that could only be achieved by filling our souls with His glory.
Praise the Lord.