Disclaimer - these are observations that I have had, I am not sure if this follows the philosophy of scrum, agile or whatever, but most of these insights were gained while implementing a scrum scenario.
Two is a partnership, three starts a team
For a while I thought that a team was anything more than one and that scrum could be effective methodology with even two people. I have recently adjusted my thinking to a scrum team being a minimum of three, so what happened to two and what do you call it?
For me I consider a group of two people working together a partnership - there is value in having a partnership, but some of the dynamics and value that you get from having a team is lost with a partnership.
Avoidance of a one on one confrontation
The first dynamic I see missing in a partnership is the team motivation to do better and how this is delivered to individuals that are not performing. Take two highly motivated individuals and put them together and you will typically see them continue to perform.
Now take a situation where you have two individuals, one performing and one not and the behaviour is totally different compared to a team of three or more individuals. With two people, if one feels the other is not performing it becomes a one on one confrontation. Most people avoid confrontations and so nothing changes.
Compare this to a situation where you have three people in a team, 2 performing and 1 not the dynamic is totally different, it is no longer a personal one on one confrontation but a team concern and people seem more willing to encourage the individual not performing and express their dissatisfaction as a team if they do not improve.
Avoiding the effects of Tuckman’s Group Development Theory
If you are not familiar with Tuckman’s group development theory give it a read (http://en.wikipedia.org/wiki/Tuckman's_stages_of_group_development)
In a nutshell with Tuckman’s theory teams go through these stages of Forming, Storming, Norming & Performing. You want your team to reach and remain in the Performing stage for as long as possible - this is where you get the most value.
When you have a partnership of two and you change the individuals in the partnership you basically do a hard reset on the partnership and go back to the beginning of Tuckman’s model each time. This has a major effect on the performance of a team and what they can deliver.
What I have seen is that you reduce the effects of Tuckman's theory the more individuals you have in the team (until you hit the maximum team size in which other problems kick in). While you will still experience Tuckman's theory with a team of three, the impact will be greatly reduced compared to two where it is guaranteed every time a change occurs.
It's not just in the numbers, it's in the people
One final comment - while the actual numbers of a team do play a role, the individuals in the team are even more important - ideally you want to keep individuals working together for an extended period. That doesn't mean that you never change the individuals in a team, or that once someone joins a team they are stuck there - there is value in an individual moving from team to team and getting cross pollination, but the period of time that an individual moves should be in month's or years, not days or weeks.
So why is it important to know this? Why is it important to know how a team works and what motivates them? I have been asking myself this question for a while and where I am at right now is this… the aim is to achieve the stage where the sum of the total (team) is greater than the sum of the parts (team members).
This is why we form teams and why understanding how they work is a challenge and also extremely stimulating.