A. Believe there 4wd is invincible!;
B. Believe they will never get stuck!; and
C. Don't understand the importance of tyre pressures.
Think of your tyres as a balloon. When fully inflated a balloon has less contact patch either in your hand or on the ground. It is also way easier to pop a fully inflated balloon.
Tyres are the same, offroad, a tyre at highway pressure is more susceptible to a stake or puncture for the same reason.
Dropping your tyres makes the tyres conform or mould or even grab over obstacles. It is precisely this ability to 'extend or increase' its contact patch on the ground that is the best wheeling modification you will ever do.
Dropping tyre pressures makes your vehicle drive over terrain easier cause it simply has more traction. More traction means less chance of getting stuck and less chance of digging holes due to excessive wheel spin. This significantly reduces the probability of damage to your vehicle and less impact on the environment.
What do you drop your pressures too and when?
Well that depends on so many things it is difficult to be accurate.
I drop my pressures even on high speed dirt roads. It makes my truck perform so much smoother inside the cab, and yields way more grip.
Mud, rocks, sand all will need different pressures. I will speak only on my experience with these recommendations on my 4 door jk on factory wheels and mud tyres.
Unfortunately, the best guide is when you've gone too far and you've popped a bead on your tyre!
But the diff in traction makes it worth exploring.
In sand I drop down to 16 psi, high country tracks about 20 and rocks down to 16 too.
When I run my beadlocks I drop down to 6psi, this increases my contact patch by over a whopping 60 odd%! This makes even bald tyres work well.
So don't forget your pressures once you hit the tracks, NO tyre works well on road pressures off road!