Almost all people do not choose their own value system but accept it from parents from school, from friends from TV and from books. They in general choose to accept certain values and not to accept other ones.The criteria are, for example : Personal Interest. A person who stands to benefit from affirmative action is more likely to think it is just than a person who does not stand to benefit or even to lose a place in a university on account of it.  Group Identification. There are lots more.
Logical moral reasoning: most people do not know what it is.
When you say the word logic most people think you mean something along the lines of: If A is true then B is true; i.e the laws of formal logic
But that is only one part of it.The main part of logic is the issue of plausibility.
If A is true then most people will accept B if they know that, "If A then B."
But what happens if Not B is more plausible than A? The logic would dictate that you turn around and deny your original assumption.
For example: a Devout Muslim accepts Islam because it is the religion he was born into and has seen and heard not particular things about it to disturb his faith. But then he learns that if Islam is true then he ought to go out and murder as many Christians and Jews as possible. This is however less plausible than the original assumption. Therefor logic would dictate that he denies the original assumption. Sadly at that point most Muslims are not thinking in terms of which premise is more plausible based on cold hard logic.
This is just one example. I have no intent here to pick on Muslims. The same would apply to any belief system in which the conclusion is less plausible than the premise.I could go on and on almost to infinity because study of fringe literature and cults and fringe groups is a hobby of mine for many years. It has gotten to the point that a very respectable person in Bresolv on Shabat asked me to examine a book written in Israel by someone who is supposedly walking in the footsteps of the Baal Shem Tov. Within five minutes I had already picked out three fatal flaws in his arguments.
Many religions try to present themselves as logical. And concerning original assumption they might well be.