Trivia: Among the choices first considered for Rambo was German-Italian actor Terence Hill (internationally best known for filming numerous action comedies with Bud Spencer), but Hill refused since he deemed the role "too violent."
Trivia: Brian Dennehy falsely claimed to have served and been wounded in the Vietnam War. He later apologized for the lie.
Trivia: When Rambo escapes the local jail, he slide-kicks and then elbows a sheriff's deputy in the face, leaving him lying on the floor screaming in pain. Sylvester Stallone accidentally broke the stuntman's nose in that take and the stuntman's screaming is real. The producers used the footage in the final film.
Trivia: Lee Marvin, Robert Mitchum, Gene Hackman and Charles Durning were considered to play the role of Sheriff Teasle.
Trivia: Al Pacino, Robert De Niro, Clint Eastwood and Michael Douglas were considered to play the main role of Rambo.
Trivia: In a deleted scene on the First Blood Dvd, Rambo is sitting by the fire when he begins to experience a flashback to a bar. The bar scene shows Rambo's encounter with a woman, with whom he was romantically involved. The background music playing in the bar, bears an uncanny resemblance to "Sunshine of your love" by Cream. The song has a few minor differences, but the progressive of the song is the same.
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