Macho, macho man. Whitman was obsessed with the idea of masculinity. He associated it with work, war, citizenship and politics, and stern father figures. “O Captain! My Captain!” seems to throw these all together in a blender, then pour it all into one intimate relationship between a sailor and his captain. Many scholars today recognize that Whitman himself was gay, but that doesn’t mean that the captain and the speaker are lovers. However, the relationship is indeed intimate and emotional. The speaker has a tremendous love of the captain and that bond was fairly typical of men before popular culture made it "unmanly" for guys to share sensitive and emotional feelings with each other. Notice how the speaker sees the captain as a father-figure. Is this the result of their journey together or is it something deeper?
The mention of body parts like the arms, heart, and lips make the scene a sensual one that excites the senses and makes us look more closely at the relationship between the captain and the speaker. It might be just a sailor-captain kind of thing, or there could be something else going on here.
Because the speaker calls the captain “father,” we as readers can assume (with no other information than how good fathers were portrayed in other literature from the 1800s) that the captain was fair, stern, emotionally distant yet compassionate, and decisive. Think Tom Skerritt in A River Runs Through It.