I think our government explained the reasons to fight well enough, and that is why the anti-war movement bloomed late. The public support seemed to crumble (as I understand it) when it just appeared that nothing was improving that could provide a timetable for an exit; unlike the permanent commitment to South Korea, which only had sporadic casualties, this seemed to be a permanent war.
However, once the Left got its feet under them, the narrative turned to "that we were interfering in another country's civil war" and the reporting specifically transitioned to featuring setbacks and wounded and dead troops - and attacks on how we were conducting the war.
The pressure forced LBJ out and then when Nixon was elected, the press went into the full shriek mode, just like we're seeing today for President Trump.
In 1969, after I was discharged the first time from the Marines, I decided to respond forcefully to an anti-gun diatribe by NBC's Bob Abernathy and I asked for time for a rebuttal. The Station, KNBC Channel 4, finally decided to discuss the matter with me a few days after the broadcast.
After about an hour in the Station Manager's office, I could see that I wasn't going to get to respond on air - so I asked that manager why the Vietnam reporting was so skewed: I saw only battles that didn't go well for the army, suffering Vietnamese and dispirited troops. I said that "you never show us clobbering the enemy, all the prisoners we're taking, the affection we get from the villages".
He said while smiling, "if we showed that stuff, the war would never end".
Then I was escorted out of the building.