Extraction of DNA is important because of many reasons. With the ability to remove DNA from an organism, scientists can observe, manipulate, and classify the DNA.
Scientists can identify genetic disorders or diseases from studying DNA.
Scientists can possibly find cures for these causes by manipulating or experimenting with this DNA.
Scientists can accurately sort organisms into classes because of DNA uniqueness. If we didn't have DNA extraction, it would be a lot harder to decide which organisms are different from each other.
Scientists can genetically engineer some organisms to produce beneficial things. A common example is that of insulin. Scientists can genetically engineer insulin production so that people with diabetes can live longer.