Why total entropy change must be positive?

This is rather difficult question.
To make progress, it is preferable to restrict the scope of the question.

I suggest you to first think about how heat flows between a cold and a hot body.
As time goes from past to future, heat always goes from the hot body to the cold body.
This is an experimental fact.
It is not totally true, however, since deviations can be observed at very small scales.
But for macroscopic objects, those fluctuations where heat goes from cold to hot are never observed.
So, you see that the size of the system is already a key to the understanding of the second.

The laws of mechanics at the molecular level are reversible with respect to time.
If a certain process can be observed, the same process but reversed in time can also be observed.
This is not true -apparently- at the macroscopic level.
The great number of "molecules" is the main reason for the irreversibility observed at the macroscopic level.
The "normal process" is "heat goes from hot to cold", the time-reversed process cannot be observed.
Why can it never be observed? Is it really impossible?
It depend on the point of view.
Mechanically the reverse process if perfectly possible.
The impossibility comes from the extreme difficulty (ie impossibility) to prepare an experiment where heat would flow from cold to hot.
It would imply a control of each molecule of the experiment, while in normal life we tend to "lose control".

The second law of thermodynamics looks very different from all other laws of physics.
It seems unrelated to fundamental laws of nature at the microscopic level.
It looks like it more about how we can interact with the world.

Read also about the Poincaré recurrence time.
You will see then that if we could wait an extremely long time, we could always observe violations of the second law.
The second law, the entropy increase, appears then more as a statement about what we could expect in real-life, despite the reversibility of molecular physics.

 

Hmmm regarding heat flow from hot to cold: The hot body's molecules have higher kinetic energy so we would expect during colisions with the molecules of the cold body that the total kinetic energy would tend to be shared between the molecules. I mean at least my intuition about a collision tells me that is highly unlikely that the molecule with the higher kinetic energy will receive energy from the lower kinetic energy molecule while it will transfer much less energy to the lower KE molecule during the same collision.

 

Well at least in the case of heat flow we try to explain using the collision mechanism, because there is some sort of symmetry in a collision. When particle A collides with B and trasfers energy to B then B also collides with A and transfers energy to A. If B which is in lower energy manages to transfer big energy to A then A will manage to transfer even more energy to B. Otherwise it would be like there is some sort of different laws of nature for particle A than particle B.

 

Indeed as I understand it the 2nd Law is not a law of nature as such, it's just a statistical consequence of our perception powers, of the huge number of states a collection of particles can find itself in, the states which we would considered as "ordered" (i.e. showing some discernible pattern for our perception, being temperature gradients, spatial distribution or whatever) are hugely rarer than states which, although equally probably and equally unique, do not show any discernible pattern to us. Every possible state happens with equal probability but there are so many more which just seem random than states which happen to have any kind of discernible order (while they are equally random in essence, but just not in appearance).

 

At any rate it's not a trivial question because it implies that the universe started in an extremely ordered = statistically extremely improbable state (and this means REALLY EXTREMELY IMPROBABLE), which is one of the big puzzles when we take this view of purely statistical probability interpretation of entropy. But it's the best we have by now I believe.

 

I'm no expert but if my understanding is correct it's also worth mentioning that the OP claim that "entropy change must be positive" is not correct when we consider gravity.
Gravity has the capability to decrease entropy, from a tenuous cloud of uniform cold gases it can convert it into a hot burning star surrounded by supercold empty space (a more ordered state in both the spatial distribution of the particles as well as in their temperature).
On small scales gravity is too weak so in our everyday experience we see only entropy increasing processes but if we look at the universe large scales, the processes we see are mostly entropy-decreasing, initially quasi-uniform huge clouds of particles at quasi-uniform temperatures condense in discrete stars and planets separated by voids of empty space.
I think that there is no universally accepted opinion about the role of gravity in the total universe entropy, whether maybe the entropy decrease caused by gravity on large scales could compensate for the entropy-increasing processes which dominate at small scales.