We should be critical thinkers and not trust everything just because we "saw it on the Internet". Students should care about fake news because they get better grades on projects by using more reputable resources. Everyone should want to be better information consumers and more informed citizens.
What exactly is fake news? The Merriam-Webster article below ("The Real Story of 'Fake' News" ) may give you a more comprehensive view and give you an idea of how long this term has been around. Wikipedia also offers a more detailed explanation.