Why every system tends to be more stable? An entire topic of inorganic chemistry, i.e. chemical bonding, which is also one of the most important topics, is based on the idea of stability. But whenever I ask why every system tends to get stable, I never get a satisfactory answer. People say that's how nature "wants" to be. How does a system know that it wants to get stable?
 A: A system state is called stable if the system returns to that state when is disturbed by a small amount. As well as that, if the system gets similar enough (which might not actually be very similar) to a stable state the system will transform to the stable state.
In this sense a system tends to become stable because stable states are the only states a system can remain in.
In energy terms a stable state is usually a state of lowest energy. The reason is that usually it is easier to lose energy than to gain it. Atoms rearrange themselves to lower-energy configurations and can lose the extra energy all at once or in stages in a variety of ways. It is usually harder to acquire the energy to change to a higher-energy configuration, and so the lower energy configuration is more stable. There are exceptions - ice is in a lower-energy state than water, but there is often enough available energy that ice is more likely to gain energy than water is to lose it.
A: Consider how many somethings there are in a mole. A whole lot, right?
Imagine you have a mole of something. And imagine that something has 3 states it can get into easily, and a lot of rare states. After awhile, statisticly it will be mostly in the common states. Because it's easy to get into them, and hard to get into the others. How many of the individual "somethings" are in each state depends on how easy they are to get into, and how easy they are to get out of. But once they've had time, they will be "stable". You'll have new ones getting into each state at about the same rate they leave that state.
Because a mole is a whole lot. A hundredth of a mole is still a whole lot.
We can't use that approach for human things, not as well. There are only 8 billion of us. We're all different genetically and we have different brains. The circumstances we react to are different. But sometimes it kind of applies to us too.
A: 1- Because that's the definition of stability: you can't escape it
In the words of Peter above :

In this sense a system tends to become stable because stable states
are the only states a system can remain in.

2 - Not all systems are "stable" some are oscillatory (like our star system or a single atom). But you may call these stable as well depending on how you look at it.
3 - In the chemistry context, evolution towards stability is described by the 2nd law of thermodynamics which is a consequence of statistical mechanics which relies on the law of large numbers that basically says that things tends to average out in the long run.
