Of all of our moral rules, I think murder is probably the most basic and easiest to logically defend. There’s a couple of arguments that come to mind.
First, the simplest and weakest argument is the tautological argument. By definition, murder is the unlawful killing of a person. As such, murder must be illegal, otherwise the definition is violated. Yeah… it’s weak, and I’d doubt anyone would be convinced by it, but, whatever.
Second is the social contract argument. A society is, by definition, a group of people living together under some form of order. This order is a set of rules by which everyone in the society agrees to live. Of these rules, that murder is forbidden MUST be included, as any other rule we make to order a society becomes baseless. That is, any other rule can be superseded or trumped by engaging in murder. For example, if we agree that stealing is wrong but murder is okay, a person who is forbidden to steal can simply murder anyone who disagrees with his action of taking an object he desires.
Third is a combination argument of comparing rights as absolutes vs. social conventions. If we assume the first, like with the argument above, it follows that a right to life is the most basic because any other right we may have is meaningless if we’re not alive to enjoy it. Thus, in creating a society to protect one’s rights, it logically follows to protect the most basic rights first, and as the right to life is the most basic, if any rights will be protected, that one must be.
The second part to that would be assuming the opposite, if we have no rights and they only exist as a construct of a society. A society is only successful if it has citizens that are able to live, work, and trade to further the success of a society. A society that cannot protect its citizens is unable to be productive in work and trade.