Although the criteria for determining if something is alive is far from settled, there are some guidelines available. According to Hickman, Roberts, Keen, Larson, I’Anson and Eisenhour (2008) any living organism will meet the following basic properties of life:

1. Chemical uniqueness. Living systems assemble large molecules.
2. Complexity and hierarchical organization. Living systems demonstrate a unique and complex hierarchical organization. Atoms and molecules are combined into patterns that do not exist in the non living world. The patterns build on each other.
3. Reproduction. Living systems can reproduce themselves. Life does not arise spontaneously but comes only from prior life, through reproduction
4. Possession of a genetic program. A genetic program provides fidelity of inheritance. For animals and most other organisms, genetic information is contained in DNA.
5. Metabolism. Living organisms maintain themselves by obtaining nutrients from their environments. They have a Metabolism which is often viewed as an interaction of destructive (catabolic) and constructive (anabolic) reactions.
6. Development. All organisms pass through a characteristic life cycle. Development usually features changes in size and shape, and differentiation of structures within the organism
7. Environmental reaction. All organisms interact with their environment. An organism perceives environmental stimuli and responds in appropriate ways by adjusting its metabolism and Physiology .
8. Movement. Living systems and their parts show precise and controlled movements arising from within the system. The energy that living systems extract from their environments permits them to initiate controlled movements.

@sfvpool argues that the social organism concept fails because "... Human cells cannot act on their own, whereas individual humans can...". Literally, I don't think this statement is true because cells do act independently of the organism they are in. They do all of the things listed above. For example, my white blood cells act autonomously when an infection is detected. Indeed, they are controlled by internal processes and higher level systems. But, so are all other organisms. For example, animals need water. Animals would not travel for a period longer than their maximum survival time without water. Sure, they could carry water with them but that only increases their maximum survival time without water. Eventually, they have to get to water. The second way that @sfvpool 's argument can be interpreted is that people are sentient and cells are not. I don't believe sentiency is a requirement. Remember that other animals, besides humans, have played major roles in the development of human societies. For example, horses, mules and camels for work; fish, pigs and chickens for food. Also, consider what these animals eat. I would argue that many of these animals are not considered sentient or at least have a lower level of sentiency.

@Beowulfsfriend says that it is "...A little like asking is fire alive? It grows, reproduces, eats and breathes and does other things a living organism will do...". However, using the above criteria, fire is definitely not alive because it fails the first 4 (at least) basic properties. There is even "better" example: The virus. The virus fails only the reproduction property (3).

So, my follow up question is which of the above properties does the social organism fails and why.

It's very hard to define what a living organism is. Under certain definitions a number of people, animals and so on could also be defined as a living thing. I suggest the book "More than human" by Theodore Sturgeon, a science fiction story that deals a bit with this issue.

It seems to break down immediately. Cells are parts of individual people, but society is a group of individual self actuating beings. Human cells cannot act on their own, whereas individual humans can. It sounds like the professor, or biology textbook, is trying to put forth an agenda of collectivism.

Biology is the study of life. Nothing wrong with that stated premise, it just sounds like something more suited for sociology.
A little like asking is fire alive? It grows, reproduces, eats and breathes and does other things a living organism will do.