Why should phospholipid non-polar tails be "protected" in the membrane bilayer?
What should be the correct reason for bilayer arrangement?


I'll answer your second question first, but there is an almost identical question on this site already: Why do cells have a bilayer?



There is water on the extracellular and intracellular side of the membrane. What's actually happening at a molecular dynamics level is the self-association of the hydrophobic lipid tail groups driven entropically by water. In other words the polar (hydrophilic) head-groups "prefer" interacting with the water (called the interfacial region) and the the hydrophobic tail groups "prefer" not interacting with the water. With those two preferences in play, the lipid bilayer formation we know and love emerges.


  why should we protect non-polar part, will it destroy in contact with
  polar part?


To directly address the first part of the question: no, nothing would be destroyed. The word "protect" isn't appropriate (it's a bit too anthropomorphic for my taste!). Here is a video showing the bilayer spontaneously assemble in a molecular dynamics simulation. Read the more thorough 2003 journal article for an idea of early MD simulations of the bilayer formation. As you can see nothing "bad" happens when the water collides with the lipid tails and the lipids aren't destroyed. 



Interesting read: MEMBRANE LIPIDS OF THE PAST AND PRESENT. Good animations and explanations of different membrane formations.

For an academic perspective, I'd recommend a couple of reviews: Cournia et al., 2015 and Gerit et al., 2008.