The spread of false and misleading news content on social media is of great societal concern. Why do people share such content, and what can be done about it? In a first survey experiment (N=1,015), we demonstrate a disconnect between accuracy judgments and sharing intentions: even though true headlines are rated as much more accurate than false headlines, headline veracity has little impact on sharing. Although this may seem to indicate that people share inaccurate content because they care more about furthering their political agenda than they care about truth, we propose an alternative attentional account: Most people do not want to spread misinformation, but the social media context focuses their attention on factors other than truth and accuracy. Indeed, when directly asked, most participants say it is important to only share news that is accurate. Accordingly, across four survey experiments (total N=3,485) and a digital field experiment on Twitter in which we messaged users who had previously shared news from websites known for publishing misleading content (N=5,379), we find that inducing people to think about the concept of accuracy increases the quality of the news they subsequently share. Together, these results challenge the narrative that people no longer care about accuracy. Instead, the results support our inattention-based account wherein people fail to implement their preference for accuracy due to attentional constraints. Furthermore, our research provides evidence for scalable anti-misinformation interventions that are easily implementable by social media platforms.