The basic reason for this is that Burke was a conservative. He was skeptical about the ability of people to create a perfect world and was more willing to trust the idea that centuries of experience were a better guide than theories derived from reason.
Burke did not believe that people could create a perfect system. He believed that human nature was too negative to allow this to happen. Because of this, he was suspicious of a polity that was founded on the rights of people rather than their responsibilities. He thought that an emphasis on rights would free people to follow their selfish natures to an excessive extent.
Burke did not believe that humans are able to reason well enough to solve all the world's problems through thought alone. If, for example, a new theory contradicted centuries of tradition, Burke was inclined to believe that the accumulated wisdom of the centuries was much more likely to be right than the theory cooked up in the mind of one individual. It would be okay, Burke thought, to move a bit towards that theory and see how it worked, but dumping centuries of tradition completely was too risky.
Because of these kinds of attitudes, Burke is seen as a conservative. He does not trust people to know when their rights should end and he does not think that reason is a better guide than experience.