Why would God be angry if he loves us?
If someone you love is addicted to a harmful drug, do you hate them because of the drug? Or do you hate the drug that is destroying them?
Of course you don't hate them. It's your love for them that makes you hate their addiction to the drug.
God hates sin because sin (e.g. lying, cheating, stealing) destroys the person who sins and those they sin against. God hates sin because he loves us. And because he loves us perfectly he doesn't just hate sin a little bit; he really hates it.
His wrath burns because of his love.
Some will say, "No, God does not hate sin because of his love for us. He hates sin because he is holy."
And what makes him holy?
It's his perfect love that makes him holy.
He hates sin because sin destroys those he loves. If he did not love us so much he would not hate our sins so much.
We will never be truly free until we are as brave, honest, fair and kind as he is. We will never enjoy unbroken intimacy with others until we, and they, are as trustworthy as he is.