"The Red Convertible" is a story that readers could find several claims within. It is probably best left to individual reader opinion to pick out the one theme/claim/lesson that he or she believes is most important to the story.
While I do see themes about brotherhood and freedom found in transportation, I think this story's main message is about the far-reaching repercussions of war and combat. I think that in general, when people hear about war and casualties of war, they think about soldiers that experience physical trauma. It's too often assumed that a soldier that comes home in "one piece" is good to go back to the life and the societal role that they had before. While this might be true of some combat soldiers, it isn't taking into account a person's entire health and wellness. A person's overall health is a combination of physical health, mental/emotional health, and social health. The story makes it clear that when Henry returns from Vietnam, he is not the same person. The war has changed him, and that makes sense, but it also affected his mental health. He returns a jumpy, silent, moody, and detached individual that rarely laughs or smiles. He's beyond a bad mood or slightly depressed feeling. There is something that isn't healthy about his mental state. It could be PTSD or something similar, but it is severe enough to cause Henry to commit suicide. The story has a strong message to readers that war has far-reaching consequences beyond what happens on the battlefield.