We are not really told in the book why people in the community do not know about animals. We do know that they know the word but they don't really know what it means. So we have to think about why this makes sense in the context of the novel.
One of the major characteristics of the society in this book is the fact that it is completely controlled. People have few choices and less freedom than in our world. They also seem to have fewer emotional attachments (part of the reason for no sex). I think that if they had animals, it would be harder for this to be. Think about the part where Jonas finds out about animals -- he acts affectionately towards the horse and seems to be having more of an emotional reaction than usual.
So my opinion is that having animals would make the society more free and complicated and that is why they do not have them or know about them.
In the book "The Giver" animals are not evident as part of the community. Animals are creatures that would have their own behaviors. The government controls all aspects of life. Animals are able to be controlled like people. In addition if animals existed the relationship would be established between the animals and people. Once again, the government would not always be able to control this. Animals also bring disease and contamination. They use up resources that are available for human consumption. If the animals were present it would alter the balance of the society. Therefore, the government does not allow them in the community.