Why did the US find it impossible to defeat the Vietcong?

There were a number of problems facing US forces when fighting the war in Vietnam. Perhaps one of the biggest problems that they faced was the fact that the Vietcong were fighting using guerrilla tactics: fighting on a small scale, taking independent, irregular actions.

The Vietcong depended on stealth, concealment, and surprise attacks and ambushes. Guerrilla warfare spread as Vietminh soldiers who were trained and armed in the North – the Vietcong, returned to their homes in the south to assassinate, ambush and sabotage. Unlike conventional wars in which the Americans may have fought, the war in Vietnam had no defined front lines. Much of the fighting consisted of hit and run attacks, with the guerrillas striking at government outposts and then retreating into the jungles.

Most of the US soldiers were also caught out by booby traps set up by the Vietcong. These ranged from simple holes in the ground to metal spikes covered in poison or human excrement. Despite their sophisticated weapons, the Americans could not eradicate the skillful and determined rebellions of the Vietcong.
Another thing that made fighting the war difficult for the Americans was the uniform that the Vietcong wore. Their uniforms consisted of black pajamas and shirts, with straw hats. This led to a great lack of trust among the Vietnamese and the Americans, as they were unable to distinguish between real Vietnamese civilians and Vietcong soldiers in disguise.
The Vietcong were also able to remain well hidden with their extensive underground tunnel system, which reached 250 kilometers in length. There were underground kitchens, weapon stores, dormitories, hospitals and rest areas. These tunnels made it increasingly difficult for the US forces to find the Vietcong.
By 1966, the Americans began a series of ‘Search and Destroy
Missions’ in order to hunt down the Vietcong. The problem was that, by doing this, they began to loose the trust of, and ‘alienated’ the Vietnamese civilians. More importantly the American public began to doubt whether or not they were the ‘good guys’ in this war and grew increasingly dissatisfied with the nations war policy. The American government began losing the support of the public once they witnessed reports about the war and events such as the My Lai massacre.
The unfamiliar terrain and conditions in Vietnam also made life more difficult for the US forces. The intense heat made it difficult for them to see where they were going, carry weapons and move swiftly. As much of Vietnam was covered in jungle, swamp and paddy fields, it soon became clear that the terrain was unsuitable for tanks.