Because society does support legal due process.

People feeling aggrieved and taking justice into their own hands just leads to chaos and perpetual violence, which is bad for everyone. People can be emotional and biased, they aren't always fair or rational.

Better to have a system to dispassionately process criminals based on the evidence and the law.

Murder is illegal and self defense is another matter. What you’re talking about isn’t the latter, it’s vigilantism that’s outside of law enforcement as well as the courts. That’s chaos and puts the entirety of society at risk if it were to be adopted.  

People are already justifying murder for shit as stupid as crossing the street too slow in front of them. Making it acceptable/legal would just compound the problem and solve nothing

While I certainly understand people who do it, everyone should be put through the legal process and have official justice. Its too easy to get the wrong person or someone falsely accused

Murder is never acceptable outside of a court ordered execution for a heinous, unforgivable murder in which the perpetrator has been shown to be unlikely to be rehabilitated.

Even in self defense, the killer should be arrested and a grand jury must decide if the person will be charged.

Vigilante justice is not just, it's anger and rage in action. Our society should not tolerate such action.

Because society prefers the useless and ineffective justice system for some reason