Yes, it seems intuitively obvious, which is why mathematicians spent a long time trying to prove that the conjecture was true. It turns out The conjecture is false in a non-obvious way. The result described in the blog post is a specific counterexample: the conjecture fails, just barely, for a specific graph with several thousand nodes and edges. It's not the kind of counterexample you would intuit in your head or even on a whiteboard.