If I recall correctly, the question was first asked of me (in a vegan/AR context rather than a more general one) when I expressed interest in seeing the slightly infamous documentary involving interaction between Peter Singer and Tipu Aziz. It seemed that certain acquaintances thought even watching the show constituted letting the side down. I think my reasons at the time were along the following lines:
-To see for myself whether Singer does in fact capitulate and express pro-vivisection sentiments. (admittedly I have a fairly healthy level of scepticism regarding the editing process, so wouldn't be 100% convinced unless he had made a very clear statement) Dude went from hero to hate figure at nought to sixty on the basis of publicity before the show aired - personally I have never seen him as either, but to make any sort of judgement I need to know what someone has actually said or done rather than what someone else claims they said or did, if that makes sense.
-To make up my own mind about Singer's words and actions.
-To be informed about what the opposition, in this case Tipu Aziz, was saying.
-To reinforce my own beliefs by testing their strength and locating the weak points that need fixing. Not a fan of dead dogmas over here.
I still apply that rationale to what I read. (I don't currently have a TV, so no idea what's going on in that arena) It's why I often read the blogs of anti-vegans and born-again ex-vegans, even though they often exasperate me. I want to know what the opposition is, what I'm up against. I might take the piss sometimes, but I try to treat these folks like worthy opponents* as far as possible. I intend at some point to read Lierre Keith's The Vegetarian Myth, in among a reading list composed of different vegan perspectives, because I want to know what she is saying. At the moment I am open to any of the new wave of vegan-hater types brushing me off with 'read Lierre' and using that as an excuse to not engage. It's a gap in my armour. Meanwhile, I feel that I am strong enough not to be 'converted' by her, so why should I be afraid to read it?
I believe that many people are afraid to read or otherwise encounter views that challenge their own. Why? Is it a betrayal of your own camp to know how the other side put their views? Are your own views so weak that they collapse when being challenged? I would hope not.
*99% of my students never want to hear those words emerge from my mouth or pen again for the rest of their lives. Unfortunately I will continue to deploy the phrase until 100% learn that brushing off the opposition without engaging will lose them marks. That could take the rest of my working life...