What Makes a Team?
We tend to think that what sets groups apart from teams is the presence of a common goal that guides people's actions. If several people get together to pursue a single goal, that's a team. This is true, but not the whole truth. What ultimately turns a group of people into a team is interdependency. A group of sales representatives working for the same company shares the goal of selling the products from their catalog, but each individual is seeking to sell more than the other, to obtain a bonus. That's not a team. A group of baseball players, on the other hand, is a team not only because they share the goal of winning; they also depend on each other. The third baseman can't win the game unless the pitcher and the catcher do a good job in defense. When people depend on each other to reach a common goal, they are a team.
And here's the deal: what makes a team interdependent are the personal relationships that exist between people. We can, then, look at a team as a collection of personal relationships. We can also argue that the quality of a team's relationships is one of the most important things a leader should worry about. So how can we understand these relationships?
As always, it's hard to look at subjective entities like personal relationships with analytical eyes. That doesn't mean we shouldn't try. Let's imagine a team of four software developers working in a project: Alice, Bob, Carol and Dave. Using simple math, you can see that even though the team has four people, it's actually comprised of six personal relationships (Alice<->Bob, Alice<->Carol, Alice<->Dave, Bob<->Carol, Bob<->Dave, Carol<->Dave)
If we were to start observing the way these people interact with one another, listening to what they're talking about when pairing, keeping an eye out for how they refer to each other during team meetings, and so forth, after a few weeks, here's an example of what we could observe:
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Alice and Dave get along really well; when they pair on a story they tend to deliver faster than when they pair with others; they seem to trust each other a lot
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Bob is a very easygoing person; everyone likes to pair with him and everyone trusts his opinions
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Carol doesn't seem to completely trust Alice. They are able to work together, but Carol seems to question Alice's decisions with certain frequency
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Dave doesn't really get along well with Carol. Maybe he resents Carol's lack of trust in Alice's opinions. He argues with Carol all the time and doesn't seem comfortable when pairing with her
From this, we get to the conclusion that while most of the relationships in the team seem healthy, there is some level of friction and distrust between specific people. But how healthy is the team as a whole? Let's try a visualization:

The green squares represent healthy relationships. Yellow means there is some level of distrust, but the relationship still functions. Red means a broken link: people are not able to work well together.
Most relationships are "green". There is some noise, but generally speaking it seems like the team is fine. After all, teams are supposed to have a little friction here and there, right?
But let's look again: suppose the green squares count as fully healthy personal relationships, while yellow ones count as neutral (zero) and reds count as negative relationships that are damaging the team (thus subtracting from the total). Something like this:

Let's add the numbers again: at the end of the day there are only three high-quality personal relationships. That may imply that our team is only 50% as effective as it could be. Should we still assume that, in terms of relationships, the team is "generally OK"? If a team is a collection of individuals (and their relationships) that depend on each other to achieve success, a severed personal relationship damages not only both ends of the link, but everyone else as well. In a highly functioning team, any unaddressed instance of distrust will spread like a wildfire, destroying the team's cohesion and undermining its effectiveness.