Audio problem: When Rambo rides the motorcycle down the sidewalk he's shouting at the pedestrians to look out. The movements of his mouth don't match what you hear him say. Originally Rambo was swearing but this was changed.
Audio problem: When the Colonel arrives at the tent we hear the Sheriff say "We're a little busy this morning Colonel, what can I do for you?", but the movement on his lips does not match what we hear.
Audio problem: In the scene after Rambo holds the knife to the Sheriff's neck, we see the sheriff in the tent having his neck looked at by the doctor. The other guy, Dave, says that Rambo is now his problem. The Sheriff then replies, but the movements of his mouth do not match what he says.
Audio problem: In the helicopter scene when deputy Gault is telling the pilot "If you don't fly this thing right...." it would be impossible to hear him over the sound of the aircraft without yelling, yet Gault speaks in a normal voice.
Audio problem: After Rambo turns onto the dirt and rock road, it looks like he is shifting gears, but the sound of the engine doesn't match.
Audio problem: In the shot early on, where Teasel jumps his car and breaks a fence post, his car horn beeps when the car lands on the ground. A few shots later, when his car falls down, then flips over on the embankment, the car horn gets stuck. It's a totally different car horn sound this time.
Chosen answer: Because it's a knife that someone else is holding and can use against him. It's common for people in dangerous professions to regard their weapons as tools. For example, police officers who commit suicide by handgun rarely use their service weapon, but rather a personal firearm.
Captain Defenestrator
Additionally, I believe it is made clear during that scene that Rambo had previously been tortured at some point, and one of the tools used was a knife. So the combination of being restrained and having someone approach with a knife caused him to basically have extreme PTSD and so he attempts to escape.
oldbaldyone