Hornblower, on the other hand, is very much a proponent of personal responsibility. Indeed, he often holds himself to an impossibly high standard of it, believing himself to be accountable for things which are in fact beyond his control. Also, when he takes an action- for good or ill- he owns it, not seeking to escape any consequences that it might cause him. This is not to say that Horatio is immune to self interest: on the contrary, he is ambitious and seeks to rise in rank in the naval service. He has no desire to do this, however, by acting in ways which would be harmful both to the men under his command and to the British fleet as a whole. This is why, in the end, he rejects Captain Foster's method of leadership, which is self-serving rather than self-sacrificial.
In closing, if I had to pick one line which encapsulates the theme of this episode, it would be Horatio's response to Foster's accusation of him not knowing his duty to a ranking officer: "I know my duty, sir. And it also lies with the lives of the men." Enough said.