Whether one thinks they do or don't need an education, it is still very important to learn. Today's society depends on your common knowledge, and to be ignorant to math or science can very much ruin your life in society today. It is very important to get somewhat of an education!
A nation that is built on a foundation of education is better suited to make critical decisions and better understand the world overall. An educated populace gives its self the ability to navigate the interworkings and subtle aspects of politics, religion, science, nature, etc. In order to determine the best solutions possible. Ignorant understandings of the ways of the world and of people never lead to good things.
Why do we need a Federal Department of education? The answer is, we don't. Some people don't want to learn a bunch of things that will not be relevant in their lives. People that want to get a certain job without a diploma, degree, do not need to be schooled on taxpayer dollars. That person will be able to get a basic understand of the country on the internet. We don't need to pay for someone to go to school, and then does a job not requiring it.
Undoubtedly, education is very important; however, the question is can the government subsidize the expenses for the study of these children who can't afford to pay because their parents don't have enough salary? I believe that's very unlikely and it would further increase the tax that people pay because of the government subsidy.