Because Game Freak decided it would be that way.
In fact, Bug was weak to Poison in the first generation. However, in Generation 2, it lost that weakness. The reason speculated is because Bug is already too weak, and more weaknesses would just make it worse.
Not everything in Pokemon is logical. Some is also done for balancing, like making Bug super effective against Dark. And Normal would probably be weak to everything if the type chart was accurate.
Source: Reasoning skills
Hope I helped!