From a psychological perspective, this is a complex question to answer but the answer sheds a great deal of light and insight into the character of Bigger Thomas!
In short, Bigger pulls the knife on his friend Gus as a way to both vent and conceal the many conflicting emotions he is feeling at that moment: anger, resentment, fear, and impotence. At its heart, it is an act of desperation to exert power and control over a situation where Bigger feels no power or control.
The scene is prompted by the plan to rob Blum's deli. Blum is a white business-owner and committing a crime against a white is something Bigger has never done before. On one hand, he is excited to exert a kind of revenge for the racial oppression that he had suffered for so long. On the other hand, he fears this act because he knows instinctively that committing a crime against white will only spur more racial intolerance and injustice against him.
However, Bigger cannot share these thoughts with his friends; he fears they will judge him as being weak and afraid--which he certainly is but doesn't want to admit. To mask this fear, Bigger pulls the knife and fights Gus in an attempt to prove his power and conceal the fear and desperation that he feels.
Almost all of Bigger Thomas's violent acts can be viewed through this same lens. There are no clear cut motivations or reasons for his behavior, but rather a complex mixing of emotions of fear, resentment, anger, and lack of control and power.