The term "social science" has two aspects and sociology can display both of these aspects. Therefore, it is a social science.
First, social sciences study the human world. Sociologists study human society. They study the ways in which group membership affects people's lives. Therefore, sociology involves the study of the human world and can be a social science.
Second, the social sciences at least try to be scientific. They try to use the scientific method in studying the human world. This is supposed to set them apart from fields such as the humanities in which this method is not used. Sociologists typically do try to use scientific techniques. They typically have hypotheses and gather data to prove or disprove those hypotheses.
For these reasons, sociology is a social science.
I like to add on some of your ideas regarding sociology---Through studying society and people Sociologists attempt to come up with some of their theory like Karl Marx on his theory of Marxism, Parsons on his theory of Structuralism and extra. Regarding their different theories we can assume that these Sociologists use only scientific knowledge and techniques to analyze the society or how people behave within their society and this will surely prove their assumptions about society and people. From there, we can conclude that Sociology must be a social science in a sense that it deals with Social (People & Socience) and Science (Borrowing plus using of Scientific knowledge to prove their hypothesis about people and their society).
its related to society...thats why..!