We can imagine a continuous line-up of ancestors, always daughter and mother, from modern humans back to the common ancestor of humans and, say, cows, and then forward in time again to modern cows. How would we then divide this line up into distinct species? Morally significant lines would have to be drawn between mother and daughter, but that seems absurd!

That's a common fallacy. Let me illustrate:

The notions of hot and cold water are nonsensical. The water temperature is continuous from 0C to 100C. How would you divide this into distinct areas? You would have to draw a line between neighboring values different by tiny fractions of a degree, but that seems absurd!