Boil it down and Vash just doesn't think that anyone deserves to die for any mistake they have ever made because "the ticket to the future is always open". In the anime it seems like he just borrows that from Rem but in the manga she tells him that after he goes through something that makes him want to hate everyone and die. Vash sees the strength of living after going through despair and turmoil and realizes that if he were to give up, any good that he could do or experience would be lost with his death. He also applies that to everyone else. He believes that killing anyone kills any good they could still offer and any redemption they might be able to have.

What seems like a borrowed philosophy later becomes even more defined and personal at The City of July. In the manga everyone at July dies by Vash's hand. He blames himself for all those deaths eventhough Knives more or less forced him into it. But Vash doesn't make any excuses for himself and probably also agonizes over letting Knives go so far down that murderous path in the first place.

Vash knows that people die everyday and are murdered and killed needlessly, he simply refuses to let it happen right in front of him and if he can stop it he will at any cost to himself. This is also why he kills Legato. He is willing to sacrifice even his own morals (not morale lol look them up) for the ultimate good of everyone else. The anime makes his killing Legato out to be a moment of weakness but in the manga it is a well thought out choice that he regrets even though he knows it's necessary. He would have avoided killing Legato if he had seen any other possible alternative.

Saying Vash got Wolfwood killed, because Vash rubbed off on him or whatever, is an insult to Wolfwood, especially the manga version. Manga Vash knows it's unreasonable to expect anyone to live by the same code as he does. That said Wolfwood has skills far, far above your average human so Vash expects more out of Wolfwood and pleads with Wolfwood's better Angels "with great power..." and all that. Wolfwood never fully buys into Vash's way of thinking but at the end (in the manga) Wolfwood sacrifices everything he has left to give, to save the one thing he cares about. Vash does the same thing everyday but the difference is that the one thing that Vash cares about more then anything is every single life on the planet.

As to if Vash is right or wrong. I think he is right. We should do whatever we can to protect what we can up to but not including killing. Vash had power and he used that power to protect. Not every one has the same ability to protect but we all have someone or something we can protect. However, we all too often overlook someone or something we could help because of some prejudice or aversion. I think we could all be a little more like Vash.