Buddha's teachings indeed represented a departure from many traditional Hindu beliefs, but it's important to clarify the points you've mentioned. Here’s how Buddha's teachings opposed certain Hindu beliefs:
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Rituals: Buddha taught that rituals and ceremonial practices were unnecessary for attaining enlightenment. This contrasts with traditional Hindu practices, which often emphasize rituals as essential for spiritual progress.
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Reincarnation: Buddha did acknowledge the concept of rebirth, but he taught that the cycle of rebirth could be escaped through enlightenment, which differs in emphasis from some Hindu interpretations. While both religions share the belief in reincarnation, Buddhism places less emphasis on the caste system and the associated rituals that can come with Hindu beliefs about rebirth.
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Nirvana: Buddha taught that nirvana (or enlightenment) is achievable and represents the cessation of suffering and the cycle of rebirth. While Hinduism also has concepts of liberation (moksha), the paths and interpretations of these concepts can vary significantly.
The statement "He taught that people should lie" is not a correct representation of Buddhist teachings. Instead, Buddhism emphasizes right speech, which encourages truthfulness and honesty.
In summary, Buddha's teachings challenged the necessity of rituals and emphasized a personal path to enlightenment that differed from the traditional Hindu approach.