عَلِيٌّ كَاتِبٌ، الْحَمَامُ طَائِرٌ
Ali is a writer; the pigeon is a bird.
Both are statements, but absent a special context they share no obvious relevant theme in their subjects or predicates. Using wāw could suggest a connection that the speaker has not established.
Rule: The fact that both are declarative does not by itself make coordination suitable. A meaningful unifying relation is also needed. Complete disconnection may concern either type of utterance or the lack of thematic relevance.