>> I beg to differ. Most people decide what their purpose is. It may not be a rightous reason. It could be totally selfish but it is still a reason. <<
We all have free choice - I do not deny this. I am saying that very few people who have lived have lived the way they wanted. Either by because of persecution, afraid to disappoint their family and friends, or simply out of fear.
>>Since GOD is said to be all powerful, he created the world, and men, why would he/she allow men who seek to disprove his existance to do so. <<
God gave us free will. The story in Genesis 3 is a parable on free will. The moment I give you choice you have the choice to do either good or evil. Again, we have free will to believe in God or not. It's our choice - to be good people or to be full of hatred and violence towards each other. We must accept the consequences of free choice.
>>Since GOD has shown himself to be vengeful, why does he not just smite down those people, along with people who do not believe in him.<<
Think then why God would create something just to destory it?