It can be powerful just to say something like: "I don't agree with that"
Direct refutation of what they have said suggests that you are open to discussion in light of further evidence, and invites people to find new arguments; whereas, saying that you fundamentally disagree makes your position much clearer.
Related: if you don't want to do something, providing the genuine reason you don't want to can avoid some pretty frustrating fights over whether you should do it. At the very least, arguments tend to be relevant.
Providing the reason might, of course, provoke other fights, or be embarrassing.
Direct refutation of what they have said suggests that you are open to discussion in light of further evidence, and invites people to find new arguments; whereas, saying that you fundamentally disagree makes your position much clearer.