What would be a reason for not citing a reference?
Thank you for your question about sources which you would not cite.
In general, you want to make sure that you are not plagiarizing anyone when you are using someone's ideas, words, images, or other work. To make sure you haven't plagiarized, you should err on the side of caution and cite anything you have included in your work that was not created by you.
Here are some types of information that are not cited, or may only be cited in-text and not on your References Page.
1. The only thing that you would not cite in some capacity (either in-text or on the References page) is what is considered Common Knowledge. Common knowledge is facts that most everyone knows such as Abraham Lincoln wrote the Gettysburg Address, Anne Frank hid from the Nazis in an attic, Nike's slogan is "Just Do It", or photosynthesis is how plants convert sunlight into energy. These are facts, not opinions, that most people are aware of and so you do not have to research these facts in order to mention them in your paper. If you are concerned that your facts may not be common knowledge, you can always look them up and then cite them.
2. Classical Works: There are some types of sources that APA requires only in-text citations and are not represented on the Reference page. These are: "references to classical works such as the Bible and the Qur'an, whose sections are standardized across editions." (APA Publication Manual, 6th ed. pg. 174). Below you will find a link for instructions on how to cite classical works.
3. Personal Communication: APA considers personal communication as not recoverable data, so it does not belong on the References page and should be cited in-text only. Examples are: memos, e-mails, discussion boards, personal interviews, phone conversations, and so on. If you do use some form of personal communication in your research, then you would cite it with the initials and last name of the communicator, and give as exact a date as possible. Example: J.J. Smith (personal communication, October 31, 2016). If the personal communication is archived and retrievable to people other than you, then you would cite it on your References page as well as in-text.
Visit the APA Help guide for more examples.