How and why Darwin conclude that life stems from common orgins and ancestors?

Answer 1

Darwin discovered through observations of nature that the natural world was not built as-is, as was previously thought, and that species had lived that are now extinct. Eventually he figured out the mechanism by which these changes occur and after that it wasn't a huge leap to look at a horse and then a zebra and a giraffe etc and realize they came ultimately from one ancestor because they have inherited traits which are the same.

That, in other words, the family tree of life on earth forks.

If you can see the similarities between a horse and a zebra and a human and another primate, you can see the similarities between all mammals, all animals, and eventually (with modern genetics) all life on earth, including plants, insects and microscopic life.

Answer 2

Darwin observed similarities in anatomy, embryology, and fossils among different species, suggesting a common ancestry. He proposed that these similarities were the result of descent with modification through the process of natural selection, where certain traits were favored due to their adaptive advantages. This led him to the conclusion that all life on Earth shares a common origin and can be traced back to a single ancestor.