Sure, but in the process of that we have to make sure we're not simply assuming we're right where we're not. What someone's really saying when they say "that's your opinion" or "that's my opinion" is that they don't consider your argument compelling and aren't interested in continuing the argument. You're right that it's a conversation ender, but people have a right to end conversations. Maybe to you that conversation sounds like you trying to explain that 2+2=4, but to them it sounds like you won't shut up about 9/11 being an inside job. Perspectives aren't absolute even if truth is. We should try to remember that and draw humility from it.
Oh, I hang in a state of constant oscillation between arrogance and self-doubt. But in general, I prefer to be correct and let "right" sort itself out. But yes, I do get exceptionally annoyed with people who go on and on about things like ... well, 9/11 being an inside job. I consider that one of a range of possibilities - it's clear people had to conspire to make what happened happened - I don't feel that we can be sure about this. It's kind of like people who talk about UFO's coming from Venus. "When you are unclear about what UFO means, we don't really need to talk about your grasp of the habitability of Venus, do we?" "Extraordinary claims require extraordinary evidence"; "assertions made without evidence may be dismissed without proof." There's a considerable number of tools to filter out the bullshit you don't need to deal with. Not wanting to deal with the remainder, though - well, you may have every right to not deal with it - but not dealing it is rarely the most productive course.