Language is a result of evolution, I don't consider it a sign of man's natural tendency to be political.
I don't really see why the origin of language is relevant. Assuming it is merely a result of evolution, it is still an essential quality of human beings. A creature without the potential to use language just isn't human. This capacity to use language is what allows us to agree on a common goal and work toward it together. That would seem to be pretty close to the classical definition of politics to me.
That said, I'm not sure that we should think of language as just a random product of the evolutionary process. Traditionally, I think the ability to communicate with others has been taken to be a result of our having been created in the Image of God, in which case there is nothing random about it.
Basically, I consider man's politicalness the tendency to be in other men's affairs; stealing, coercion, etc. Again, I consider this the result of ancestral sin. I have not heard a rebuttal yet.
In that case, there may just be some problems with definitions. Obviously, things like stealing are a result of original sin (there is no difference between Eastern and Western teaching on this issue, by the way), but I don't think anyone who says that man is political by nature considers stealing to be the essence of politics. Coercion is a little more complicated. As a result of the Fall, it is sometimes necessary to resort to coercion in order to defend justice, but even coercion is generally not seen as being essential to politics. For example, St. Thomas argues that there would have been government even without the Fall. This is because government for him is primarily defined by its goal, which is the good. Even without the Fall, according to St. Thomas, men would have organized in order to pursue the good. You have to understand that the classical and medieval writers have a completely different understanding of politics.
I have also heard the statement that we are all de facto reliant on others, and this somehow annuls any claim to rights of man. I don't see how the conclusion follows.
Well, I think it shows that the anthropology behind the "rights of man" is false. Here, we start with some sort of isolated, worldless self. In reality, we are never isolated or worldess. Instead, we are always already in the world and involved with other people. The isolated individual is a fiction, and so using it as a starting point for talking about social organization is always going to lead you down the wrong path. We are so involved with, and even determined by, the actions of others, that there really is no such thing as "the individual." In any case, I have not seen any compelling reason to believe in human rights.
Another point to consider is the fact that Christian doctrine tells us that there never was a time when only one isolated individual existed. Even before time began, the first thing we see is three things: the Trinity, three Persons in relation. So, at the deepest level, I think Christianity points toward the primacy of relationality. Relationality is coprimordial with individual persons. In contrast, the whole anthropology behind individual rights, it seems to me, is based on the assumption that relationships are somehow secondary or less real than individuals.
Also, as mentioned above, the Church has always thought of herself as a public society. If politics were only a result of the Fall, why would Christ come to found a political community? This would seem to show that we are essentially political, which in itself is a good thing. However, in practice this tendency toward politics has been corrupted by the Fall, which is why we see things like abuse of power and the need for coercion. The Church, as a society based on charity, corrects this and shows us what true community really looks like, but this still means that man's political nature is inherently good.