Triangular lattice quantum antiferromagnet has recently emerged to be a promising playground for realizing Dirac spin liquids (DSLs) -a class of highly entangled quantum phases hosting emergent gauge fields and gapless Dirac fermions. While previous theories and experiments focused mainly on S = 1/2 spin systems, more recently signals of a DSL were detected in an S = 3/2 system α-CrOOH(D) in Ref. [1]. In this work we develop a theory of DSLs on triangular lattice with spin-S moments. We argue that in the most natural scenario, a spin-S system realizes a U (2S) DSL, described at low energy by gapless Dirac fermions coupled with an emergent U (2S) gauge field (also known as U (2S) QCD3). An appealing feature of this scenario is that at sufficiently large S, the U (2S) QCD becomes intrinsically unstable toward spontaneous symmetry breaking and confinement. The confined phase is simply the 120 • coplanar magnetic order, which agrees with semiclassical (large-S) results on simple Heisenberg-like models. Other scenarios are nevertheless possible, especially at small S when quantum fluctuations are strong. For S = 3/2, we argue that a U (1) DSL is also theoretically possible and phenomenologically compatible with existing measurements. One way to distinguish the U (3) DSL from the U (1) DSL is to break time-reversal symmetry, for example by adding a spin chirality term Si • (Sj × S k ) in numerical simulations: the U (1) DSL becomes the standard Kalmeyer-Laughlin chiral spin liquid with semion/anti-semion excitation; the U (3) DSL, in contrast, becomes a non-abelian chiral spin liquid described by the SU (2)3 topological order, with Fibonacci-like anyons.