Carbon is a core structural element of known life. Scientific sources consistently show that carbon forms the backbone of the main biological macromolecules because it can make stable, complex bonds in ways crucial to biochemistry. The claim is accurate as stated, though it refers to life as known on Earth and does not imply carbon is the only essential element.
Caveats
The claim is about known Earth life; it does not prove that all conceivable life everywhere must be carbon-based.
Carbon is essential but not sufficient by itself: life also depends on other elements such as hydrogen, oxygen, nitrogen, phosphorus, and sulfur.
Some lower-quality or ideological sources appear in the source list, but the conclusion is independently supported by authoritative scientific references.