Euglena do photosynthesis using the same basic process that plants use. They also move around and eat, as do animals. But you are right that they are not classified as either of these. That is because they are unicellular. “Uni” means one (a unicycle has one wheel). In order to be classified as a plant or animal, an organism has to be multicellular, or made of more than one cell. Since it is a unicellular organism with some plant and animal characteristics, it is called a protist. Plant cells have walls. There’s no cell wall around a Euglena’s cell membrane, so it is a protozoan. It used to belong to the kingdom Protista. Now most scientists think we should stop using that kingdom.

Keep in mind that humans make classifications in order to organize the amazing complexity of the world. The natural world does not fit neatly into all of our classifications. We can be pretty sure about how closely related things are by analyzing their DNA, but there’s no magic number that means they belong in the same kingdom, order, or family.

If you want a real challenge, read up on Volvox. It can do photosynthesis. It can live singly or in a colony. It can swim around with flagella. Is it a plant, an animal, an algae, a protist? You make the call.

Most species of Euglena have photosynthesizing chloroplasts within the body of the cell, which enable them to feed by autotrophy (making energy-containing organic molecules from inorganic raw material through the use of an energy source such as sunlight), like plants. However, they can also take nourishment heterotrophically (making use of food that comes from other organisms in the form of fats, carbohydrates, and proteins), like animals. Since Euglena have features of both animals and plants, early taxonomists, working within the old two-kingdom system of biological classification, found them difficult to classify - not because they had features different from an animal and different from a plant, but because they had some features that were animal-like and some features that were plant-like. So could they be both? It was decided that they could not, and in fact other species that had both animal and plant-like characteristics were discovered and so in 1866 Ernst Haeckel added a third kingdom to the Animale and Vegetabile of the old taxonomic system: the Kingdom Protis

Plants are multicellular organisms with cellulose cell walls. Depending on the definition, plants may or may not need also to enclose the developing new plant in an embryo (if this definition holds, then green algae are not plants; otherwise, they are).

Animals are multicellular organisms held together by a specific protein called collagen.

Euglena is single-celled, and the cell is enclosed in a semi-rigid protein sheath, not a true cell wall but not a simple cell membrane. Euglena is entirely unicellular, has no collagen and no cellulose, stores energy in paramylon bodies (not starch as plants do).

Euglena is photosynthetic, but the origin of Euglena's chloroplasts is taken *from* a green alga, not directly from cyanobacteria/chloroxybacteria as plants and green algae are.

From Wikipedia, Euglena is a genus of "unicellular flagellate protists." The key to why they're not considered plants or animals is in the word "unicellular," which means the entire organism consists of one cell. This is very different from a plant or an animal, both of which are comprised of many different "specialized" cells that carry out different functions!