But if the only thing that convinced you of a thing is an analogy or emotional appeal, and if in being convinced you learned nothing about the underlying argument the analogy is supporting, you are susceptible to being convinced by similarly compelling analogies or emotional appeals that may or may not have any grounding in a solid argument.
I’m not claiming that people can’t be convinced this way. I’m pointing out that this form of persuasion is problematic and insufficient. “Argument from analogy” is considered a fallacy for this reason. It can lead people to take on new beliefs for bad reasons, even if the position they take is the “right” one.
While emotions absolutely influence our beliefs, it’s not accurate to downplay the role of formal logic, which is often implicitly invoked by emotional dialogue. The two are not mutually exclusive, and they work together.
For example: in a discussion about climate change, a purely logical presentation of facts about the temperature of the ocean and receding ice is not compelling without understanding the implications. Painting a picture of potentially cataclysmic outcomes and mass extinction events and migrations evokes an emotional response that is also necessary for humans to take action.
In this example, either one without the other can be problematic. Pure facts logically presented are hard to interpret, especially if you aren’t a climatologist. And if there is no logical foundation whatsoever, the argument is on shaky ground and the person who now believes it will have no reason not to believe the next emotionally compelling thing.