There are the two obvious reasons - the boy prefers to spend his time with the old man who shows a level of interest and caring for him. In comparison, the old man also enjoys the boy's company; in fact, throughout the entire time he is battling, the old man wishes very much that the boy is with him.
The other example is in the old man's relationship with the fish. His reference to the fish as his brother shows a great level of respect for his competitor, but also shows the reader that the old man has established this fish as his companion during this voyage. Lacking another actual person to talk to, the old man frequently addresses the fish in conversation.