If you have been asked to make the argument you listed above, there are several ways to argue that loyalty to a state (e. g., a region) should supersede loyalty to a nation. Here are a few:
1. A "nation" may be an artificial construct, made up of different and highly distinct "states" or regions that have very little in common with one another. For example, China is a nation that claims that Tibet is a part of the nation, even though most Tibetans would presumably prefer to be independent. The same is true of relations between China and Taiwan. Sudan recently split into two different nations because the two main states or regions could not live in peace with one another.
2. When a nation is indeed composed of incompatible parts, violence and bloodshed are often used to keep the parts together. Many conflicts taking place in the world today are conflicts within "nations" because some "states" want to secede. Enormous loss of life might be prevented if more such "states" could become separate nations. One recent example of an intranational conflict involved the decades-long war between the Tamils and the rest of the nation in Sri Lanka.
I think that two key elements of this essay need be made clear from that very start: You need to ask yourself WHY loyalty to the state should supersede loyalty to the nation, and you need to define what you mean by state -- in the United States? in other countries? The second question will provide your context for the topic and the answer to the first question will be your thesis statement.
In your body paragraphs you can then discuss each of the reasons you come up with as to WHY loyalty to the state is more important. You could discuss local connection to others in the area, having more personal power on the local level, or the importance of the smaller political//social region as it relates to the larger one.
You could approach this by looking at the sorts of issues that arise when people are more loyal to their nation than to their state. We can see problems like this in Iraq and Afghanistan right now where so many people are loyal to their tribe or other "nation" and do not really care about how that loyalty tears their state apart.