Why was it so threatening for the white community if a black man raped a white women?

A black man didn't actually have to rape a white woman to qualify for a lynching in the post-Civil War South.  Even the perception of sexual interest on the part of a black man toward a white woman, whether it be through overly familiar conversation, or any sort of action that could be perceived as flirtatious, could be a dangerous proposition.  Emmett Till, the young man who was murdered while visiting his uncle in the South, was kidnapped, beaten and killed simply because someone thought they heard him whistling at a white woman.

Prior to the Civil War, in the world of large plantations and wealthy owners, the plantation owner's wife's primary functions were to oversee the household, take care of slaves who might become ill, and function as a gentle, well-dressed trophy at the occasional ball or barbecue.  Fast forward past the Civil War into the era of Jim Crow laws, and then into the early 20th century, and there was still a perception in the South that white women were to be protected, and black men to be feared. Additionally, the perception of the black male as being inherently dangerous probably dated back to the era when slaveowners lived in constant fear of slave revolts.  The Southern ideal of the pure, genteel white woman, an ideal that dated back to before the Civil War, was at the root of the accusation by Bob Ewell against Tom Robinson.  When Ewell wanted to cover up the beating of his daughter, he chose an accusation that would play upon these entrenched cultural assumptions; he accused a black man, Robinson of assaulting a white woman, his daughter, knowing full well that most of the people of the community would automatically perceive Robinson as guilty.