The issue is, it's not really possible to do that in many if not most cases. For example, suppose you're a political reporter, and a politician makes a claim that happens to be objectively false. Do you merely report that the politician made that claim, or do you report that the politician made that claim and that it is false, or merely report that the politician made a false claim without repeating it verbatim? All of those things are only reporting verifiable facts in this scenario, but they all give different impressions as to the character of that politician.

The obvious answer one might take is to go with the second option, and say that one should just report all facts available to you and relevant to an issue, because choosing what truths to say and what not to say still presents a biased picture even if every statement you make is a true one. But this is not a solution, because you simply cannot and will not have room to say every true statement about something, and you have to decide which things are relevant and irrelevant and to what degree, and your personal biases will influence these decisions regardless of how much you try to avoid that, because there's not a way to objectively measure relevance.

Further, you do not actually know what is objectively true. You might say that a politicians statement is verifiably correct or incorrectly, because you believe that to be the case- and be wrong about that. There's a greater likelihood that you'll scrutinize something said by someone you disagree with, and so you'll unintentionally portray your favored candidate in a better light, just because you don't have time to verify every single sentence (and for that matter, since you're a reporter and not actually someone collecting and analyzing the raw data, you won't generally be equipped to verify things yourself so much as ask someone who you believe is reliable, and who therefore probably agrees with you and shares your biases), and you're more likely to check if something is true if you already suspect that it isn't.

Perhaps then, to be safe, you might only report that the politician said "x", and not comment on if it is true. Beyond the obvious issue of helping to spread lies even if you don't technically yourself say that they are truths, just that the person that said them did so, you still don't have room or time to repeat every single thing that politician says. If you report on the more absurd statements of one politician and the more reasonable statements of another (which it may be hard not to do subconsciously, because absurd positions that align with your own won't seem as absurd to you and therefore not as important to inform people of), you once again create a biased narrative out of nothing but true statements.

Finally, even if you avoid all this, you still introduce bias by when and where you say things. Stories run on the front page are more likely to get seen and read. TV broadcasts made when people are awake and at home are more likely to be watched. YouTube videos that appeal to the site's algorithm are more likely to be seen, etc.

It is simply impossible to run an actually unbiased new source. You cannot say the whole truth, because you neither know it all nor have room for it all nor have the capacity to give it all equal attention. And you cannot say nothing but the truth, assuming you say anything at all that is, because your knowledge and sources are not infallible. The best you can do is state your biases up front, to the best of your ability, so that people know what kind of perspective your reporting comes from.