Han is a loner (“Solo”), traveling with no one but a hairy, six-foot tall Yeti-like creature named Chewbacca (another animal sidekick to diffuse homoerotic potential), and unwilling to investigate potential human relationships.
At first he refuses to speak directly to Luke, and when he lets down his guard sufficiently to acknowledge Luke’s existence, he calls him by the diminutive “Kid.”
We wonder what he’s afraid of, and so does the Girl, brassy Princess Leia (Carrie Fisher): “Your friend is quite a mercenary!” she snaps at Luke. “I wonder if he really cares about anything. . .or anybody!”
Han finally warms up to Luke: they fight together, rescue each other, hug; at the end of the movie, Han asks Luke to go away with him (“I could use a partner”), and, when he refuses, decides to stay with Luke. But now Luke has competition in Princess Leia, who is “infuriated by” (that is, infatuated with) Han. She manages to insert herself into every shot featuring the two together.
When they are slamming against each other in a jubilant bear-hug, she squeezes between them, so they are actually hugging her.
When Han tries to walk off with his arm around Luke, she squeezes between them again.
Even in the last scene, when Han and Luke receive medals and then turn to receive the applause of the Rebel troops, the camera pans out to present the illusion that Princess Leia is between them (she is actually standing behind them).
Director George Lucas, not well known for accentuating the homoerotic potential of his films, worked very hard to ensure that Han and Luke never connect in any substantive way. What was he afraid of?