They became increasingly invovled as they didn't want the Domino of Vietnam to fall.. The president of South Vietnam- Diem was assasinated and thats when the escalation of the war began to take place. LBJ didn't wanna be seen as the president to lose the war. So when you look at it, look at the instability of the south, the growing numbers of the VC, the fact that America didn't wanna look like they were losing the war and by that point they weren't they were winning battles strategically but losing them pyschologically particularly with TET (68).
“Moreover, the United States began involving itself directly in the political affairs of South Vietnam, at first supporting and then contributing to the overthrow of the repressive regime of President Ngo Dinh Diem in 1963. From that point on, events moved swiftly as U.S. intervention mushroomed both politically and militarily” (Dudley 13).
I hope that helped..