What is the ruling on someone who said to his father, "It's my responsibility, do not swear by other than God," meaning that swearing by other than God is polytheism and that his father should follow him in abandoning this act, then he retracted his statement fearing that he would fall into sin if his father were to swear by other than God?

It is apparent that you are suffering from excessive waswasah (whispers/obsessive thoughts), and what you mentioned falls under the category of waswasah and its effects. There is absolutely no blame upon you for what you said to your father, and you incur no sin if your father swore by other than Allah. What is incumbent upon you is to entirely disregard these waswasah, to cease preoccupation with them, to cut off from indulging in them, to avoid asking about them, and to supplicate to Allah to cure you of them.