Why is algae not considered under plants though it is photosynthetic? Is it microorganism?

Although algae are plant-like in preparing their own food, they lack many structures like roots, stems, leaves, tissues, etc. Algae usually survive near the water surfaces or underwater. However, most of the plants can thrive on land. Plants are multicellular, while algae can be either unicellular or multicellular. Due to such differences, algae are placed in a separate kingdom, and are considered different from plants.