Yes, you need science. Science helps us to solve problems logically, and to understand the world around ourselves. You personally will probably need to use it in the future to make decisions about what medical tests and treatments you and your loved ones should be getting, to help you decide what mode of transportation is best for you to use, to help you make good choices about what foods to eat, to help you decide which technological devices to buy...the list goes on and on.
Additionally, everyone needs to understand some science in order to be a good citizen. Many political actions affect the environment, both locally and globally. Being able to grasp the consequences of these political actions can help you decide how to vote. Without some science knowledge you are at the mercy of others. It's always better to be equipped to make your own informed decisions.