One of the most important things to watch out for in arguments both our own and those offered by others is the influence of bias or vested interest. Both are variations on the same sort of problem, although there are differences that require mentioning each separately. Bias occurs any time that facts are interpreted in a way that unreasonably favors one position over another; vested interest is a cause of bias in which one will personally and specifically benefit if people adopt a particular position.
Ultimately, some sort of bias is always going to exist after all, we are all humans and we all have our passions, desires, and preferences. We wouldnt even be debating particular issues unless we cared about them in some way, so the very fact that we are participating in a debate or discussion is itself evidence of some sort of bias.
Having a bias, however, is not the same as allowing ones reasoning and arguments to succumb to bias. An important hallmark of critical thinking is that a person makes a sincere effort to recognize and acknowledge their biases, ultimately taking them into account when weighing evidence and logic so as to ensure that those biases dont unfairly tip the scales in an inappropriate direction.
It is also important to listen when someone points out possible biases because, quite frankly, we often arent good at noticing when we have biases that influence our thinking. Biases inappropriately influence our reasoning, but much of the time we tend to think that our perspective is the only correct one a perspective which everyone should have. Thus, whatever biases we have represent biases everyone should have.
A vested interest is a particular cause of bias which occurs not simply when one unreasonably favors a preferred perspective, but in fact favors a perspective which provides them with specific benefits. An obvious example of vested interest would be anyone who is paid to promote a product in commercials. It would be absurd to trust their testimony that one product is better than the competition because they obviously arent expressing an independent judgment they are only saying what they have been paid to say.
There are also many ways in which a person can have a vested interest which arent quite so obvious. A person might, for example, discount allegations of unethical or illegal conduct against a company they have stock in. They might also favor any reports that improve the image of the university they once attended on the assumption that anything which makes their old school look better must therefore make them look better as well.
We can also identify backwards-looking examples of vested interest because people seem to have a strong interest in defending decisions that have already been made no one wants to be wrong, after all. Thus, people are inclined to focus on highly favorable reports about cars they have purchased and dismiss negative reporting about the same cars because doing so helps them maintain the perception that they made a good decision in that purchase. Similar behavior can be seen when it comes to political candidates or political parties voted for.
It is important to keep in mind that not all examples of bias are also examples of vested interest and not all cases of vested interest result in bias. A person might quote a reporter who is biased and thus transmit that bias without realizing it. A person might have a strong vested interest in something but still manage to write about that matter in a fair and even-handed way.
Neither bias nor vested interest are themselves fallacies or flaws in reasoning they are simply a part of being human. They can, however, cause a person to commit fallacies or other flaws in reasoning as they seek to defend a position that depends more upon their biases than upon logic.
Because of this, charging a person of having a bias does not therefore refute or undermine any of their arguments. Everyone has a bias, so saying that a particular person has a particular bias isnt news, and alleging that a particular bias is the real reason for them holding a particular position isnt very persuasive. If you can demonstrate that there are no reasonable arguments for their position, then you might have something but that, obviously, requires dealing with the arguments they offer independently of whether there is bias or not.
In short, then, bias is probably something that is most important when evaluating your own arguments because only you can really tell to what degree your position has been influenced by your biases. You can ask another to double-check their biases, but beyond that all you can do is address their arguments as stated. If you refuse to do so and simply allege that their arguments, being biased, dont merit response, then you probably arent acting in good faith.