Actually Darwin's explanation is random heritable variation and natural selection. He does not assume all life-forms descend from a common ancestor. We don't even know what that means. Given how early in the earth's geological record single cell life forms exist, it appears that life arose as soon as conditions on earth were not totally inhospitable to life (e.g. too hot to sustain the necessary chemical reactions inherent in carbon based life-forms). If life is so robust, then there is no need to assume a common ancestor. In fact, eukaryotic cells are evidently the combination of two different earlier life forms.
But this is typical. The first thing to do when denouncing a scientist is to slander him with words he never uttered.
Clearly there is evolution. But it isn’t random mutations über alles. Lamarck May have invented epigenetics with no way to prove it. But he had a point. Environment changed species. Now we can prove it.
Simplest epigenetics example is that if you place a pony embryo into a horse uterus, the foal becomes significantly larger than a pony when grown.