The assumptions of a science should be valid. If you examine the assumptions of many economic theories, you will find that many are idealistic and unlikely to hold true in the real world. One example of such an assumption is that humans will always make rational choices. You can probably think of examples from your life where this does not hold true.
Many renowned scientists, such as the physicists Richard Feynman and Neils Bohr, consider controlled experiments to be an essential part of science. Experiments are important for two reasons. First, they can show cause-and-effect relationships between phenomena. Second, they are repeatable, meaning if you doubt the claim of one experimenter you can repeat her experiment and see the result yourself. In this respect, though it is a social science -- a science that is applied to the studies of society -- economics is not a true science because economics often cannot rely on experiments to test its theories. For the most part, economics relies on observational data, though experiments are sometimes done in economics.
A science is a method of understanding and predicting events in the real world. If economics is a true science, it should be able to help people in understanding the phenomena of the world and the laws of economics should hold true. However, many essential economic laws have large amounts of empirical evidence against them. Take for example the Coase Theorem. This theorem states that legal rights will flow freely through legal exchanges as long as there are no transaction costs for exchanges. But in real world situations, with no transaction costs for such exchanges, the Coase Theorem fails to hold.
According to geologist David L. Ozsvath, some people make a distinction between "hard" and "soft" sciences. In contrast to the traditional "hard" sciences like physics and chemistry, a "soft" science is a science that does rely entirely on controlled experiments. "Soft" sciences are not as rigorous as traditional scientific disciplines, and often forgo strict definitions and facts in favor of open-ended theories. In this sense, many consider economics to be a soft science.