It's a tricky question, because in the case of:
You are beautiful.
No, I'm not.
one could argue the person is being modest; whereas with:
Things will get better.
No, they won't.
we could say the person is being pessimistic or glum.
You're trying to find a single word that encompasses all three of your examples. You might consider the word naysayer. Collins defines this word as:
naysayer (noun) someone who opposes something or says no to it
although naysayer often implies a negative attitude rather than a modest one.
Another possible word is contrarian. One definition found at Wordnik reads:
contrarian (noun)a person who expresses a contradicting viewpoint, especially one who denounces the majority persuasion
It also depends on the tone in which the person denies what you are saying. They might disagree with you politely and humbly, or they could do so childishly. In the latter case, you might call them argumentative, but remember: there is a difference between argument and contradiction, as this very funny sketch points out:
An argument is a connected series of statements intended to establish a proposition...
Argument is an intellectual process; contradiction is just the automatic gainsaying of
anything the other person says.
Hmm... maybe gainsayer is your best choice.