West Point of View: Often say that the relationship Buddhism and Hinduism between the two is like the relationship between Judaism and Christianity in some ways. Christianity was inspired by the life of a Jew and Buddhism was inspired by the life of a Hindu .
Response: Buddhism is considered a part of Hindu tradition because Buddha never said I am starting a new religion—he only reformed what was already in existence.
Buddha became a monk in the Hindu tradition and then he shared the path to monkhood with everybody. He never discarded the Gods or Goddesses. He put the Buddha (the enlightened) first, which was already how it was.
In earlier days, people would do animal sacrifices, and Buddha condemned all that. He said you should not do this sacrifice. In any religion, there is always some such interpolation. Though it was not the original practice of the religion, later on, these things get into the religion. And then people think this is the religion. They leave the philosophy and hold on to the practices. These become causes of contention and then sects develop.
Even in Buddhism, there are Hinayana and Mahayana. Buddha never created Hinayana and Mahayana. There are 32 sects of Buddhism, all mushroomed later on. Which is the one Buddha created? He did not create them at all. He just reformed what was already in practice.Monks were wearing saffron in this country; he wore the same thing. Monks were shaving their heads; he asked all his monks to shave their head. So everything in Hinduism—like begging alms, asking for food, letting go of the ego—Buddha followed the same thing