This is a pretty big topic and the question is misleading. It isn't asking whether God exists but instead is asking why we should not believe in God. It is like whether we should not believe in Ambrosia (food of the Gods).
There are many reasons that one should not believe in a God. Placing faith in something outside of yourself absolves you of responsibility if you can convince yourself it is something that God "wants"... being prejudiced against others because they do not believe the same way that you do.
It is anti-progressive (once again if you convince yourself that it is God's will)... if God wanted me to fly he would have given me wings. Allowing faith in a God perversely dictate behaviour ... ask Aqsa Parvez - you cannot because her father and brother killed her. An honour killing which brought dishonour to an entire country.
People who believe in God tend to have a very narrow understanding of God. Imagine that you one of several people standing outside a house. Each looks into a different window and then describe what a house is. One person will say that is a place that you prepare food. Another will describe it as a place to sleep with a third might say nothing is there because the room that person looked at was unlit.
Part of the problem is that we do not know what God is. Some have this vision that God is some guy with a white beard looking at us (or is that Santa Claus). In my case I like to conceptualize God to be like a river going to the sea. Each of us are droplets within that river. While it is silly for a single droplet to dictate the direction the river will flow, a stream of droplets can cause the river to meander.