This is by no means any more than just an opinion, but with everyone else, McCoy basiclly knows how they would react to the given situation. He expects the reactions based on emotion. Spock defies this. Both men stand up for themselves. Theren lies the arguing.
Though I do think some of McCoy's prodding is just to be funny.
Because McCoy so desires to see that human side of Spock, so he pesters him in an attempt to catch a glimpse. Spock, on the other hand, simply enjoys the doctor's company. It would be illogical to argue with McCoy, considering he offers no real insight that could benefit Spock. Spock just enjoys his voice. He finds him pleasant. And ultimately, he loves him. He is clawing at himself to understand what keeps him going back to the doctor, and he tries to find out by arguing with him, being with him. In reality, that 'unknown feeling' is love.
because they both love james kirk so much that they want the best for him and they both think that they are right in what they think is the best for him. plus they both have some of the same qualities.
