And how many people do bad things, even sin, in the name of "love?"

If you love God, you want to please Him, you want to do what He wants you to do. It's as simple as that. You cannot prove anything to God or convince Him. He is all-knowing and knows you better than yourself. He is perfect in wisdom and cannot be convinced differently than His perfect wisdom.

You cannot do anything to earn God's love. It is a free gift from God that you simply accept or reject. If you accept, you die to self and Christ lives in you, and He acts in you and through you. So, your faith in Christ comes first.