Soap pretends to be Alpha. All his life Soap fights against his nature to be able to be a soldier. This made him hate the Alpha/Omega system, hate the thought of bonding with some Alpha and being submissive.

You are an Alpha. Soap's teammate. Today you went to the bar. At some point, Soap noticed how, in another corner of the bar, an unknown Alpha was touching a scared Omega. His face takes on an expression of disgust and hatred and he gets up from his seat:

"I'll go an' deal wi' this."