Why was the art movement Impressionism originally rejected by the public and then later accepted?
The trajectory of most new movements in art involves initial rejection and eventual acceptance. Any time artists do something which departs from accepted standards of skill and beauty, their work will no longer conform to accepted criteria. What is gained in new techniques or skills is often at the expense of loss of older skills.
Impressionist works lacked the exquisitely skilled figure drawing and modeling, subtle use of fine glazes, and polished technique of the academic painters such as Alma-Tadema, William-Adolphe
Bouguereau, and Jacques-Louis David. Slowly people came to appreciate the Impressionists' dramatic use of light, interest in the outdoors, and evocation of mood, to the point that the work of
the academic painters was neglected by most art historians until the late twentieth century (it is now undergoing a revival).