A sound or habit can irritate a person without making everything associated with it worthless. Being startled by a rooster’s crow is one experience; insulting the creature is a separate choice. The listener can learn self-restraint rather than acting on every annoyance.
In فَإِنَّهُ, فَ connects the reason to the preceding instruction, إِنَّ adds emphasis, and the pronoun هُ refers to الدِّيكَ. The wording thus gives a clear reason for the command to guard one’s speech.