It is always dangerous to try to interpret songs, but I'll try anyway, since you asked.
The song appears to be about people (sometimes political, sometimes personal) who tell lies disguised as the truth. The things that they are saying are bad, "atrocity" and "hating on your loved ones", "poisonous pen" make that clear. But they are also deceptive "ill-fitting illusions". And, the people want to appear passionate but they aren't "martyr with a mission, but the motive is insincere"
The chorus ... I think(?) is what Lerche wants these people to do. Cough up their hearts ... which is where all this is coming from. "Swallow their pride" is a saying that means humble yourself, normally in order to ask forgiveness or something. "Shut up" ... quit writing these things, "restart without those oxymoronic lies" ... oxymorons are famous for being a way to hide the truth of a thing through words, which is what lerche has been talking about all along. For example a "benevolent dictator" is an oxymoron, and a lie, because it implies that a dictator can be good. Some would consider "war on terror" another example because wars cause terror.
But .... a song is a very personal thing... I am probably totally wrong :D