Execution is brutal and barbaric, certainly all of the current US methods are.
Some methods like lethal injection hides some of that and let's you pretend that it isn't if you close your eyes and wish very hard. For the prisoner though it can be horrendous, what with the hunt for a vein and the distinct chance of being in absolute agony yet paralysed and unable to show it.
So it's not so much "don't be barbaric" but "on a superficial level don't seem barbaric to me, to the prisoner you can be as barbaric as you like".
"I mean you might linger on for a bit."
Compared to the electric chair, lethal injection or gas the chances of lingering are minimal.
"what's worse is that with all their medicine they still can't find a humane way of killing someone."
They can, but they won't use it. Hypoxia using nitrogen, it would work in about 15 seconds and far from causing pain the victim would feel euphoria. It's often used to kill lab animals as it doesn't affect the tissues and causes minimal distress.
That it's not used for humans raises some very interesting points about barbarism and the true nature of execution, that is that it's not about removing the criminal from society but people actually wanting the executed to suffer.
"Firing squad, they aim for your head, one of them is going to hit the mark, it's quick instant job done."
Not in America, they all aim for the heart and all will hit it. Death is still very quick though due to shock and severe blood loss.
"I read that they use silver tipped bullets or something."
That is apparently the name of the type of bullet, it's not actually got a silver tip.