When you hear powerful evidence or arguments that should get you to revise your beliefs, not only do all sorts of cognitive biases fight the changes but so do the social factors of status and face saving. Perhaps I've long been a vocal proponent of X which implies Y, and you show me that Y isn't always true. It's very hard to just straight up admit "ok, I'm not a hardcore Xist anymore." There's a status loss in letting yourself be convinced.
For a long time I thought that I was stronger than this, that saving face only mattered as much as I let it matter. I wish I could freely admit when I've been convinced, but I often can't manage to. [1] Instead I'll finish a conversation defending my earlier beliefs and only later start acting on my new ones.
After a discussion where someone didn't admit to any change of mind, I'll often see them later having changed their behavior. So now if I'm trying to persuade someone I don't focus on securing verbal agreement. Instead I just try to be as convincing as possible, and notice if they come around later. [2]
(I also posted this on my blog)
[1] This is not a helpful trait: I'd like other people to let me know when I'm wrong or when they have evidence I'm not considering, but if they never get the satisfaction of knowing they've convinced me they may just feel like they've wasted their time, and not try in the future. So I'm working on it.
[2] Keeping people from feeling personally invested in one side or the other of an argument is probably also helpful: I understand discussions are much more likely to convince bystanders than participants.
Group social norms about the appropriate status changes applied to someone who changes their mind are important. Personally I respect someone more if I notice they change their mind publicly, but I'm sure I'm in the minority, and it was only through deliberate self modification that I acquired this trait.
Also, a classic overcoming bias blog post on these topics:
http://www.overcomingbias.com/2008/06/overcoming-disa.html
Notice, too, that public figures with a reputation for frequently changing their minds tend to be the subject of mockery and ridicule even in academic circles. When, for instance, the name of Hilary Putnam comes up in philosophy discussions, it is not uncommon to read or hear a sarcastic comment noting that he has successively embraced and abandoned several different positions on a given question over the course of his career.