This paper studies the problem of stabilizing discrete-time switched linear control systems (SLCSs) using continuous input by a user against adversarial switching by an adversary. It is assumed that at each time the adversary knows the user's decision on the continuous input but not vice versa. A quantitative metric of stabilizability is proposed. Systems at the margin of stabilizability are further classified and studied via the notions of defectiveness and reducibility. Analytical bounds on the stabilizability metric are derived using (semi)norms, with tight bounds provided by extremal norms. Numerical algorithms are also developed for computing this metric. An application example in networked control systems is presented.