In the ancient world people did not have baby formula to put in bottles. So it was much healthier for babies to be breast-fed, even if it was not their own mother’s milk, than it was for them to have plain cow‘s milk (which was only available in the spring and summer anyway). Besides, without refrigeration or pasteurization cow’s milk often had germs in it. That could kill babies or make them sick.
Poor women also often had wet-nurses, so that they could go back to work in the fields or as servants or textile workers. But poor people couldn’t pay their wet nurses very well. A lot of poor people’s wet nurses tried to nurse too many babies at once, and often the poor babies died.
Bibliography and further reading about wet nurses:
Wet Nursing: A History from Antiquity to the Present, by Valerie Fildes (1988, currently out of print).