Arial v Helvetica is an interesting example, because Arial was designed basically as a cost-efficient alternative to Helvetica. So, the reason you'd choose between the two is exactly the thing the original comment was complaining about – licensing! They were designed to be metrically compatible... meaning, the character widths and spaces are exactly the same. This means that switching to Arial won't affect the layout of your document. This was more important when things were more analog, but it's still important with digital documents: for example, it could mess up the number of pages, which would affect meta content or create line breaks that seem meaningful but aren't. Additionally, having things like a widow (a word by itself on a new line) can disrupt the visual flow and draw focus to or away from content in ways you don't desire.
But just because those two typefaces are quite similar (and the reason to pick between them is largely financial/convenience) doesn't mean you'd never want to have more fine-grained control over the text you're working with.
You mentioned security. When I'm editing this comment, 0 and O are very different (the zero has a slash through it), however when I hit save they look quite similar. (But because we're all using system fonts on HN, it might be different for you). While it's often just a stylistic choice, in many situations the two characters would be indistinguishable and that would be an issue, which is why someone might choose a typeface where characters are significantly different. Think a password you have to transcribe.
If you know your font will be used in a quite small size, you may want one that is optimized for being read at tiny sizes. If you're displaying something technical, a monowidth font is better suited.
And all of this focused on utility for the most part; I'm leaving out all the reasons you'd want it for stylistic reasons. If you're trying to make people feel at ease, you may want typeface where the end of the strokes are rounded, for example. Sometimes you want people to feel a certain way, in the same way you modulate your tone when talking.