I always think of it as more of an infinite ladder; take one step up and there's always another. If someone says one site isn't biased their opponent will say "how do you know it isn't biased?", proceed to make a list of things that they feel proves it is biased, and then ultimately reveal that the list is based on stuff they read from a site they think is unbiased, thus adding another step to the infinite ladder. And then their opposition does the exact same thing.
I don't think it's quite such an impossible mess to weave through. Yes, every source is biased but the
levels of bias vary considerably as well as the overall
commitment to be impartial and objective. We can learn to detect these levels and commitments (as well as lacks thereof) which in turn enables us to glean glimpses of truth from a variety of sources all of which suffer from a type and degree of bias.
The journey out of any 'rabbit hole' or ideological indoctrination starts with honestly accepting that sometimes we prefer highly biased sources, and avoid others, because they justify our own personal beliefs or personally convenient narratives. All sources fall somewhere on the scale of roughly 4 levels of bias in my personal and subjective analysis:
Sources:
(1) To whom commitment to integrity, objectivity, factuality, accuracy and impartiality is genuinely a matter of pride (not just a slogan) and represents the foundational principle governing their work. Political or ideological leanings of the authors or sponsors of these sources are allowed but consciously and resolutely kept from undermining this 'scientific'/'high journalistic' commitment.
(2) Who believe in integrity, objectivity, factuality, accuracy and impartiality while having more or less obvious blindspots due to a particular political or ideological leaning. Sometimes they demonstrate deliberate partiality but mostly seek to report facts, although often edited with a slant.
(3) Who publicly state that they uphold integrity, objectivity, factuality, accuracy and impartiality -- and pursue an appearance of impartiality and professionalism in their knowledge-products -- while their work is predominantly political or ideological in nature. Sometimes they report competently on neutral topics and occasionally demonstrate an absence of political or ideological bias.
(4) Who produce blatant propaganda or who openly disseminate political or ideological beliefs.
Over the decades of my earthly existence sources that fall under 1 have always been few and far between. However, today, they seem almost non-existent. Aside from solid scientific journals, I think
NZZ (regrettably mostly in German) remains rather close to 1 from amongst news media. CNN and Fox News are both 3 (3- and 3+, respectively) in my analysis. The likes of Ben Norton and Breitbart are squarely 4 along with Russia Today and the news media of the People's Republic of China. BBC, The Economist and Al-Jazeera fall somewhere between 2-3. AP, Reuters and Deutsche Welle are 2. And the list goes on.
These are obviously personal and subjective valuations, but you get the drift. To put it simply: If you know the key biases and pitfalls of Russia Today and Breitbart, you might be able to glean facts from even their highly slanted stories without falling for any of the propaganda. Throw a wide net and learn, critically and intelligently, from all perspectives whilst blindly believing in none.