Kiba's actions towards Shino is significance (if you squint really hard, which I have) in many sorts of ways. The most common solution to the question, "Why does Kiba thinks Shino is trying to act like the team leader?", is simply: Kiba has some alpha complexes (which is why I chose this site name, hint hint).
Now you ask, "what the hell is an 'alpha complex'?" Then I would laugh and reply: You silly bitch; it's a system of the animal kingdom of which the dominant male or female who runs his/her pack. There is an alpha male (sometimes female; ex. Tsume is the alpha female in the Inuzuka Clan, since the whereabouts of Kiba's father are unknown--probably deceased,) in every pack, and, as mentioned, they are basically the leader. However, often times, their positions will be challenged by another male, and they would battle to see who is stronger. So, this is basically to show whose boss.
In more humanistic terms, you can refer the "alpha" male or female to the highest position in the social latter. For example, the boss of a company. They are the leader of the company and basically run the whole program.