Easy, yes. Necessary that I do so, no. I won't bother to do your research. Try a web search. Google reports 213,000,000 results for "veterans hated". Knock yourself out.
I did that search.
Top hit is a quora forum in which someone who works at the VA deals with nasty phone calls because many veterans do not trust the VA but they talk about how to help them. Not a great example.
Second hit is a pewresearch poll talking about how non-veterans and veterans see veterans in terms of loyalty, hard working, etc. Nothing about hatred.
The third hit is a History channel article talking about the indifference veterans faced coming home from Vietnam due to the fact that many vets served a term and came home by themselves and not with a unit. It also highlights the government showed towards veterans. Not the civilian population.
Fourth hit is an article by The Atlantic talking about why some vets do not particularly care for the "Thank you for your service" comment by civilians.
Next is a twitter comment about Republicans not liking vets because of a specific vote.
And the next one is about Sons of Confederate Veterans being involved in hate groups.
Digging four pages in I came across a reddit discussion in which many people point out that the Vietnam vets were not despised by the public so much more than the fact that vets returning from duty came back so on an individual basis. While there were some highlighted moments of antagonism towards vets the counterculture readily welcomed returning vets who joined the anti-war movement.
To be honest, if you could link in specific examples and research that could tie in the issue of suicide and how veterans are treated by the civilian population, in other words being hated, that would actually go towards highlighting perhaps why there is an increased suicide rate among our veterans.