why did God became man?

What better way to show your love to the ones you created than to come to Earth and live and die among them?

Jesus had to be both God and man for a couple of reasons. He had to be true man in order to be under the law. God made the law for people not for himself. If Jesus wasn't true man, he wouldn't be under the law and unable to keep it perfectly. "When the time had fully come, God sent his Son born of a woman, born under law, to redeem those under the law so that we might receive the full rights of sons." He also had to be true man in order to die. As a human, he was mortal and therefore could die for our sins. He had to be true God in order to be perfect. Humans cannot be perfect since they are brought into this world sinful. "Surely I have been sinful from birth, sinful from the time my mother conceived me." He also had to be true God in order to redeem us. Had he just been human and been perfect, he would have only saved himself. He had to be God to take on the sins of the whole world, and pay for them on the cross. Hope this answers your question. Peace.