What he reports to us is that there is no longer a need for such an anthem because the Rebellion has already been completed. However, being a satire, allegory and using so much propaganda, we know there are other reasons.
He quits using the anthem because of the language in it. It encourages a freedom and a place wherein animals rule themselves. He has been enjoying his power and wants to keep it. He doesn't want any ideas floating in their heads about rebelling against him.
Napoleon says that “Beasts of England” was a song of the revolution and was no longer needed. The real reason he bans it is because he does not want another revolution.
Old Major, the revered old boar, has a vision for England which the animals transform into Animalism under the banner of the patriotic tune, “Beasts of England.” It’s their rallying anthem throughout the revolution, and they enjoy it afterward. It includes such stanzas as this.
Riches more than mind can picture,
Wheat and barley, oats and hay,
Clover, beans, and mangel-wurzels
Shall be ours upon that day. (Ch. 1)
The animals are inspired by this tune to work harder, kick out the man, and run their own farm. Under this new farm, they will have all the food they want, the song reminds them. They have been oppressed, but they will soon live a life of luxury.
Napoleon and the other pigs allow the song to continue for a little while after the revolution, in order to keep the animals motivated. It is sung at meetings, and soon the tune is known throughout the land. However, soon they tell the animals to stop. They give a good, sound, logical reason (the pigs are good at those). The real reason, though, is that “Beasts of England” begins to be rebebllious again, and the animals are rebelling against the pigs. When no one dares to speak his mind, Clover sings “Beast of England.”
The other animals sitting round her took it up, and they sang it three times over—very tunefully, but slowly and mournfully, in a way they had never sung it before. (Ch. 7)
Napoleon tells the animals that “Beasts of England” is banned because it “expressed our longing for a better society in days to come” (Ch. 7). Since now they have the perfect society they longed for, it is no longer needed. Of course, this is quite the opposite of the truth. The song has been revoked because the animals are well aware that they were sold a bill of goods, and their society is far from perfect. They traded one corrupt master for another. The new boss is just as bad, if not worse, than the old boss. The pigs realize this, and that is why they forbid the song.
You can find the answer to this towards the end of Chapter 7. Napoleon himself does not explain why this is, but Squealer does tell us. He has come out to tell the animals that they have to stop singing the song after they have sung it three times. They have been singing it because Clover started to sing it as a way to express how she feels about how much better things are now than under Jones.
But Napoleon has Squealer make them stop. He says that the song is no longer needed now because the Revolution is over and it was a revolutionary song. He doesn't want the animals singing songs about freedom and self rule because he wants all the power for himself.
In Chapter 7, Napolean commands his dogs to brutally murder several animals who confess to various crimes against the farm. After the executions, Clover and the other animals stand on the hillside looking out at the farm and think about old Major's speech. Clover cannot express her feelings, so she begins to sing Beasts of England. In a melancholy tone, the other animals being singing with her. After their third time singing the song, Squealer arrives with two dogs and tells them that Napolean has decided to abolish the song. Squealer proceeds to explain that Beasts of England was the song of the Rebellion and the Rebellion has been completed. Squealer says that the execution of traitors was the final act of the Rebellion, and the ideal society that was described in the lyrics has come to fruition. The animals' protests are silenced by the bleating sheep. Minimus, the poet, then writes another song which replaces Beasts of England.
Napoleon abolishes Beasts of England because he does not want the animals to believe that Animal Farm is not the ideal society. The lyrics to the song express how animals live a terrible life full of drudging work. Napolean fears that the animals will realize that their lives are horrible and rebel against his rule. The song also encourages independence, and he wishes to maintain his dictatorial role as leader of the farm.