No, I disagree with the statement. Computer science is one among the finest course available in engineering career. Perceiving a career in this branch enables one to develop an attitude for problem solving with simple logics as algorithms. once a person starts developing a logic for solving a problem continues doing it and this of course is a stable profession when chosen as a career option.
To answer your question of unstable profession, tech service related jobs are quite unstable, in case of recession lots and lots of employees and lose the job