When someone ignores us or treats us badly, our tendency is to get angry with them, or else treat them the same way they've treated us. Like Samson in the Old Testament, we say (at least in our hearts), "Since you've acted like this, I won't stop until I get my revenge on you" (Judges 15:7).
But God isn't like that (and neither should we be). God loves us in spite of what we are! You are right: From a human point of view, it doesn't make sense -- but it's still true! This doesn't mean He overlooks our sins or pretends that they don't exist -- not at all. But as the old saying reminds us, "God hates the sin -- but He still loves the sinner."
How do we know God loves us? We know it for many reasons -- but the greatest reason is because He sent His only Son into the world to die for our sins. We deserve only God's judgment -- but because of His love for us Jesus Christ took upon Himself our judgment and our Hell. The Bible says, "For God so loved the world that he gave his one and only Son, that whoever believes in him shall not perish but have eternal life" (John 3:16).