This is because the whole point of strategic management is to gain a competitive advantage for your firm.
A firm's strategy consists of the set of related actions that its management takes in order to improve the way the firm performs. Every firm wants to improve its performance to the point where it is superior in some way to its competitors. This superiority is the firm's competitive advantage.
When studying strategic management, you are learning how to analyze and devise your firm's strategy. You are learning how to look at the various strategies your firm might take and to determine which of them will give you a competitive advantage. You are also learning about how to implement the strategy that is selected.
The purpose of studying strategic management, then, is to be able to do a better job of creating competitive advantages for your firm. Therefore, the concept of competitive advantage is central to this field of study.