It's not simply that people believe specific things, but that they define themselves in terms of what they believe.
And in fact, it's often the case that people invest in specific beliefs not because they've reasoned their way to that conclusion, but simply because they've effectively picked it off the rack of possible beliefs as the one that most clearly represents whatever image of themselves they wish to promote - it's the position held by smart people or enlightened people or trendy people or moral people or strong people or whatever.
So if you try to argue against their belief, you face two immediate and generally insurmountable obstacles.
First, they're psychologically invested in the belief, so if you call it into question, you're not just threatening the belief - you're threatening their self-image. Anything that casts doubt on the belief by extension casts doubt on their self-affirming presumption that holding the belief demonstrates their intelligence/morality/whatever.
And second, since it's likely the case that they didn't reason their way to the position in the first place, they can't becreasoned away from it anyway. So itvinevitably shifts back to their psychological investment in the position, and your attempts at reason are a distraction at best.