I don't agree with you!

I'd say this could become an appeal to authority fallacy if you were to cite yourself as an expert, then use that as the sole basis for disagreeing. For instance:

Abby: Dinosaurs went extinct 65 million years ago.

Brad: I'm a scientist, and I disagree with you.

Abby: Why?

Brad: Because I'm a scientist and I know about this stuff.

That said, if someone claims to be an expert on a topic, but can't or won't explain their reasoning, I would be suspicious of whether the person even has the credentials they claim to.

You and Dr Bo are both right; any potential fallacy would be in the reasoning  rather than the bare statement "I don't agree with you!"

I guess the question more related to "I don't agree with you" as the entirety of the counter argument, as opposed to inviting an ad hominem backing etc. That is, unbacked, although understanding there would always be a reason. It may simply fall on into the problem, classically, that no matter how well constructed your argument, your opponent need not believe in your position? But if the response was rooted in a cognitive dissidence, then what?

I would consider this situation an argument by pigheadedness . I think this would only apply in a situation where the person has already attempted and failed to refute the person's point.