Why does the Second Law of Thermodynamics hold true?
According to second law of Thermodynamics,

During spontaneous process:

$$ ∆S_{total} &gt; 0 \ or ∆S_{total} = 0 $$

So total entropy is positive.

But $ ∆S_{system} \ or \ ∆S_{surroundings} $ may be less than 0.

Which $ \implies $ any one of $ ∆S_{system} \ *OR* \ ∆S_{surr} $ may be less than 0. 



Now, according to Big Bang theory, the Universe, soon after existence , is expanding more and more and so - its entropy is increasing.



 Why entropy should be positive to occur a spontaneous reaction?

An example first:
• Heat flow is unidirectional. That is, from higher to lower temperature.
Similar to it, all Physical or Chemical Process will tend to proceed spontaneously in one direction only(unless altered by some external agency). 
Hence,
Spontaneity is the potential to proceed without assistance of external agency. 

Now, Entropy means randomness or disordered behaviour.
And there is always a tendency for the system's energy to become more disordered. An example would be diffusion.
Where gases diffuse and become more chaotic. And during the expansion of our universe, its entropy increases.

So, we interpret that entropy for a spontaneous process increases, till it reaches maximum. And our universe having a positive $∆U$ and gaining entropy in the direction of spontaneity. 

$∆S=0$ at equilibrium. 

If $∆S$ is negative that would mean that reaction or process is going opposite to the spontaneous direction, and which is not possible in case of our universe.