Learn English – Adjective for things that in theory can exist but in real world cannot exist

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.

One adjective that may work:

entitled
adjective
believing oneself to be inherently deserving of privileges or special treatment.
"kids who feel so entitled and think the world will revolve around them"

^{Source: Google define operation on entitled}

This describes someone who thinks they deserve something. It can be money or other things.

If someone is always looking for a way to get something, we might say they are opportunistic.

opportunist
noun
a person who takes advantage of opportunities as and when they arise, regardless of planning or principle.
"most burglaries are committed by casual opportunists"

opportunistic
adjective
"the calculating and opportunist politician"

^{Source: Google define operation on opportunist}