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The two main hypotheses for the origin of whales are the terrestrial hypothesis and the aquatic hypothesis.
The terrestrial hypothesis suggests that whales evolved from a terrestrial ancestor that gradually became more adapted to an aquatic lifestyle. Evidence supporting this hypothesis includes the fact that early whale ancestors such as Pakicetus had legs and lived near the shore, suggesting that they were semi-aquatic. Additionally, the fossil record shows a gradual transition from early whale ancestors with legs to later species with more aquatic adaptations, such as smaller hind limbs and a more streamlined body shape.
The aquatic hypothesis, on the other hand, suggests that whales evolved from a fully aquatic ancestor that was already adapted to life in the water. Evidence supporting this hypothesis includes the fact that early whale ancestors such as Ambulocetus had limbs modified for swimming and a tail fluke similar to that of modern whales. Additionally, some molecular evidence suggests that whales are more closely related to hippopotamuses than to any other group of mammals, and hippopotamuses are fully aquatic.
Overall, the evidence supporting each hypothesis is still subject to debate and interpretation, and it is possible that whales evolved through a combination of both terrestrial and aquatic adaptations.
