Question: Why wouldn't Bambi's mother tell him that the Great Prince of the Forest is also his father?
Question: Is it true that Disney made this movie as a way to protest guns and/or hunting?
Answer: No. As with most Disney films, it's based on a book, in this case a 1923 Austrian book entitled Bambi: A Life in the Woods. There's no evidence that the book was chosen for any more than the quality of the story.
Answer: Probably so he would not think he is superior to the other fawns and try to lord over them. She would have told him about his father when he was older. This is also a literary plot device by setting up a dramatic reveal at a crucial time (right after Bambi's mother is killed) that Bambi learns his father is the Great Prince. This has a greater emotional punch.
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