Q: Why non-selective B-Blockers are preferred in portal hypertension instead of selective B-Blockers?

Answer:

The non-selective β-blockers (like propranolol, timolol or nadolol etc) are preferred because they decrease both cardiac output by β1 blockade and splanchnic blood flow by blocking vasodilating β2 receptors at splanchnic vasculature.

Reference:

Talwalkar JA, Kamath PS (2004). "An evidence-based medicine approach to beta-blocker therapy in patients with cirrhosis". Am J Med 116 (11): 759–766