In answering the question of why algae, fungi and microbes are not plant life, it is first necessary to understand what a plant is. The online dictionary www.dictionary.com defines a plant as: "any member of the kingdom Plantae, comprising multicellular organisms that typically produce their own food from inorganic matter by the process of photosynthesis and that have more or less rigid cell walls containing cellulose... some classification schemes may include fungi, algae, bacteria..."
It's clear from this definition that some scientific classifications do include algae, bacteria, and fungi as members of the plant kingdom. Definitions and classifications of all living things have changed over time. The first classifications were simple: if it moved it was an animal, and if it didn't, it was a plant! Later classifications recognised there were many more differences than whether the thing was anchored or not, and also recognised the fact that some plants are not anchored, and some animals are.
Algae are not now considered plants, even though most contain chlorophyll and carry out photosynthesis as plants do. They are different to plants in that algae have no roots, leaves or stems, and there is no tissue differentiation in algae. They are also aquatic, and they also differ in their reproduction method (producing gametes from single celled chambers instead of multi-celled chambers). Algae are usually classified as belonging to the Protista Kingdom, but earlier classifications put Protista as a sub-group within the Plantae Kingdom.
Microbes are tiny single-celled organisms that are visible through a microscope, but are too small to see with the naked eye. Microbes include bacteria, viruses, and some fungi, protozoa and algae. They are not now classified as plants because there is no tissue differentiation, and no roots, stem or leaves. A few are able to carry out photosynthesis, but most absorb nutrients through the cell wall. Microbes are usually classified as belonging to the Monera Kingdom, but earlier classifications have put Monera as a sub-group within the Plantae Kingdom. As noted above, some are also classified as fungi, algae, or protozoa.
Multi-celled fungi do have tissue differentiation, and you don't need a microscope to see a mushroom (although you would need one to see microbial fungi, such as the single-celled yeast). Fungi have no chlorophyll and don't carry out photosynthesis, which is the main reason they are not now classified as plants. They obtain their food from dead organic matter, or from other living things (in which case they are called parasites). Their reproductive system is also different from plants, in that they produce spores. Many fungi have a stem, and the underground structure of filaments (mycelium) could be likened to roots, but its function is different. In plants the roots draw nutrients up to the body of the plant, which is above ground. In fungi the mycelium is the body of the fungus. Fungi are usually classified as belonging to the Fungi Kingdom, but some classifications have put Fungi as a sub-group within the Plantae Kingdom.
Classifications of algae, fungi and microbes changed a great deal in the 20th century, when these organisms began to be classified as being outside the plant kingdom. As more is learned about these fascinating organisms, classifications will no doubt undergo further refinement.