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The rapid rise of Large Language Models (LLMs) has sparked intense debate across multiple academic disciplines. While some argue that LLMs represent a significant step toward artificial general intelligence (AGI) or even machine consciousness (inflationary claims), others dismiss them as mere trickster artifacts lacking genuine cognitive abilities (deflationary claims). We argue that both extremes may be shaped or exacerbated by common cognitive biases, including cognitive dissonance, wishful thinking, and the illusion of depth of understanding, which distort reality to our own advantage. By showcasing how these distortions may easily emerge in both scientific and public discourse, we advocate for a measured approach— skeptical open mind - that recognizes the cognitive abilities of LLMs as worthy of scientific investigation while remaining conservative concerning exaggerated claims regarding their cognitive status.