The question is not whether one has biases or not, but whether or not they're held captive to them. When you read a headline from let's say CNN with what sort of accuracy can you predict exactly what sort of slant the article will come with, even when such is not implied directly by the headline? It's going to be quite high because the site is held captive by its own biases.
Of course everybody is influenced by their biases, but fortunately we have the intelligence to ensure that our biases are but a component of our decision making process rather than being that process in and of themselves. Because of this when you find an individual (or organization) that makes some effort to be impartial it can be difficult to determine where they will land on many issues. As an example Greenwald is gay and lives in Brazil with his husband. The current president of Brazil is Jair Bolsonaro who has made statements such as 'I could not love a gay son; if I had one I would prefer he die in an accident.' This [1] is Greenwald explaining why Bolsonaro was elected.
It's easy to expect to see him just repeat tropes. And this is something that increasingly often the NYTimes is doing such as here [2] where they chose to publish, without elaboration: "Mr. Bolsonaro is ... a brash nationalist whose populist appeal comes partly from his use of Twitter and his history of making crude statements about women, gay people and indigenous groups." Bolsonaro won by a 10 point margin in a country that was and remains very liberal. The only reason the NYT characterization is not overtly fake is because of the use of the weasel word "partly."
Instead Greenwald acknowledged the tropes are going to make up some part of Bolsonaro's support, but then got to the important question - why completely normal and unbiased people, and even some LGBT types, would be voting for people such as Bolsonaro. Obviously he does not want to do this. We like to demonize people we don't like - it's human nature. He'd like to imagine Bolsonaro's base is just loaded with monsters and slur them all as being racists, misogynists, homophobes, or whatever else. But this is, of course, not the case. And so he ends up considering things he would probably rather not consider. And that, rising above one's biases and petty instincts, is at the heart of effective, meaningful, and responsible journalism.
[1] - https://theintercept.com/2018/10/29/the-lessons-for-western-...
[2] - https://www.nytimes.com/2019/03/19/us/politics/bolsonaro-tru...