Minors are capable of violence, therefore n some cases it could be justifiable to execute a minor. If they have committed a particularly dangerous crime, there maybe no better choice. Rehabilitation is not always an option, when someone so young commits certain criminal offenses. Each case would have to be evaluated invidually of course.
The minor would have to be closer to an adult age, and would probably be tried as an adult. If the minor was able to commit such heinous crimes at such a young age then the behavior will probably stick with them for life. If a violent sociopath could be executed as a minor and save the lives of people who he may injure/kill in the future, it would not be morally unjust to execute him/her at an early age.
Violence perpetrated by the State erodes the fabric of society by informing vigilantism and police brutality. Executing a minor is one of the most fabric-eroding tasks a society takes on. These are innocents, waifs who know not what they do and have years to be rehabilitated if they do know what they do.
To choose to execute someone means that it has been decided that they are so bad, they don't even deserve to live anymore. It means you feel they are completely unable to be rehabilitated.
But a minor is not even full developed, you can't say they are unrehabilitable when they have not even reached a stage of maturity yet.
What would you get safety? How much harm and danger could the minor cause? Executing a minor is a completely retarded choice. Minors are not yet mature. In fact, they aren't even capable of holding themselves together. If they do cause any hazards, maybe its for attention. Besides killing, there are many other ways a minor could be stopped,
There are minors who commit heinous crimes. Yet the whole idea of law that prevents people under the age of 18 from facing horrendous penalties is the fact that people under 18 have immature brains. There may be crimes serious enough that a person should not get out of jail for a very long time, but executing someone who may not fully understand the gravity of what he or she did is just plain wrong.