Arguably, the best episode that shows Kirk's obsession with the ship and command is The Naked Time.
Early TOS was very much a recreation of the late 18th century navy (though shipboard procedures were inspired more by WWII aircraft carriers) . These sailors were thousands of miles from home, thousands of miles from any form of civilization whatsoever. Their only home was that ship. Their only tie to civilization, to any form of society, was the men aboard their ship. The ship's survival meant their survival. Loss of their ship meant death, or, worse, being marooned amongst godless savages, forever lost.