Why do economists see themselves as scientists?

Well, I would say economist see themselves as scientist because it depends on hypothesis and research to thrive.

An economist is an  expert in economics, especially one who studies economic data and extracts higher-level information or proposes theories.
A scientist is somone who whose activities make use of the scientific method to answer questions regarding the measurable universe. A scientist may be involved in original research, or make use of the results of the research of others.