For example.

Someone (call him John) intentionally killed your loved one (call her Lisa, your wife) and escaped the authority.
It's 100% sure that he's the killer and did it intentionally.
You went and killed John to avenge Lisa and got caught after your act.

Do you deserve to be sentenced with a first degree murder? On a crime that would otherwise not happen if the first crime didn't exist.

The law doesn't have grey area. You either did it or you don't. In the example above, you would be sentenced as first degree murder, regardless of who your victim was. 

You justify it by not getting caught. Amateur.

No you can´t.

If you´d get 6 years for murdering a murder, the person murdering you would also get 6 years and not more.

The next time one child hits on the other child, the other child would be allowed to hit back.

That´s called anarchy and no, it doesn´t work. The whole world would die in chaos. Or maybe just get corrupted.