While memes are often humorous, they are frequently used to disseminate hate, causing serious harm to individuals and society. Current approaches to hateful meme detection mainly rely on pre-trained language models. However, less focus has been dedicated to \textit{what make a meme hateful}. Drawing on insights from philosophy and psychology, we argue that hateful memes are characterized by two essential features: a \textbf{presupposed context} and the expression of \textbf{false claims}. To capture presupposed context, we develop \textbf{PCM} for modeling contextual information across modalities. To detect false claims, we introduce the \textbf{FACT} module, which integrates external knowledge and harnesses cross-modal reference graphs. By combining PCM and FACT, we introduce \textbf{\textsf{SHIELD}}, a hateful meme detection framework designed to capture the fundamental nature of hate. Extensive experiments show that SHIELD outperforms state-of-the-art methods across datasets and metrics, while demonstrating versatility on other tasks, such as fake news detection.