Why is murder a sin unless...?

It can also be justified in self defense...the key word is "justified"

It should be noted that In Aquinas' "just war theory" murder is not argued as a moral good, but rather...a necessary evil demanded by justice. The first of the three principles that must be in place to justify war..is that it must be in response to an oppressive regime... In other words you can't start a war, only respond in turn to another country which has unjustly waged war against you.

Oh. and if you're insistent on embracing the flawed sola-scriptura arguing parameter...you won't find any evidence to support the idea.

Murder is only murder when it is illegal!

Self defense is legal as is killing someone to stop them killing others and of course in war!

Your problem appears to be that you do not understand what the word murder means!

As I recall, it's because Paul/Saul said that when God installs a leader to be in charge of you, that you should pledge your allegiance and honor what you are told to do because the direction comes from God through the leader. So if Hitler tells you to murder Jews and throw infants into bonfire while they are still alive, you should do so because it's a direct commandment from God who installed Hitler into a seat of power.

I'm sure someone here knows the exact verses in the letters of Paul.