This is broadly true. I'd definitely agree that the media has a left-leaning bias.
But you can't copare the birther movement with Trump's impeachement. The two thihngs couldn't be more different. The birther movement was a totally made-up nonsense about whether Obama was an American citizen.There was no evidence to the cotrary whatsoever other than the subtext that a black man probably wasn't really American .
I mean just think about that. He was already president at that point! Do you think anybody at all would have taken it seriously if it were a white president?
Trump's impeachement was because there was actual material evidence that he abused the power of the presidency to aid his re-election. This isn't about one side starting it, they're just two very different things.