Because it means a member of the military that he himself commands is... Stupid .
There, I said it.
We're talking about a 7ft tall maniac who can, merely by thinking about it, choke you from across the room without touching you.
And that certainly wasn't Vader's first demonstration of such.
Even if they thought he was a con, merely 20 years prior the entire galaxy knew about the Force and considered it a given.
It would be like having one of your employees in charge of running the factory telling you
"I don't believe in electricity".
First, you're astonished at the utter contempt for popularly known truths.
Second you're shocked that anyone could willfully deny a phenomenon for which there was evidence all around him.
Third, you begin to doubt your own judgement of character (which Vader probably and rightfully considers paramount to his continued rule).
Finally, it is something that would anger him that someone would both call him a liar and presume his own weakness.
scifi.stackexchange.com/users/7603/John O
Vader's comment was sardonic; the young officer taunted Vader and Vader responded in kind.
He was not disturbed, except to the extent that he was annoyed by an obviously ignorant and arrogant officer who dared challenge him.
Excerpt from the exchange: Officer:
Any attack made by the rebels against this station would be a useless gesture no matter what technical data they've obtained.
This station is now the ultimate power in the universe.
I suggest we use it.
Vader:
Don't be too proud of this technological terror you've constructed.
The ability to destroy a planet is insignificant next to the power of the Force.
Officer: Don't try to try frighten us with your sorceror's ways, Lord Vader.
Your sad devotion to that ancient religion has not helped you conjure up the stolen data tapes.
Or given you clairvoyance enough to find the rebels hidden fortre-- (face contorts, gasping)
Vader: I find your lack of faith disturbing.
Vader can only be in one place at a time
so it's possible for someone to come up through the Imperial ranks without seeing Vader's mojo in action.
Right up until the moment the Force tendrils seized his neck the officer assumed Vader was some sort of witch doctor.
scifi.stackexchange.com/users/4096/Kyle Jones
This station is now the ultimate power in the universe.
There it is; the cause of Vader's reaction.
All through his training as a Jedi, his fall to the dark side, and subsequent career, one thing would have held true - the Force as a power.
A claim of something else as the "ultimate power in the universe" doesn't just go against his training; it's something he knows to be untrue.
So when someone shows a lack of faith in the power of the Force - well, he's got to be put right, hasn't he?
scifi.stackexchange.com/users/None/
As any Sith, Vader took his Dark Side seriously.
It was a way of life, more so than a religion or ideology.
Therefore, having the most important thing in his life being dismissed as old timey superstition is... disturbing.
Remember what drove Vader/Anakin all this way.
The vision was using the Force to unite the Galaxy and bring order to it.
The officer relying on some pimped out technology as a solution was basically undermining that approach.
scifi.stackexchange.com/users/976/DVK-on-Ahch-To
I think you are right that Darth Vader didn't really care what Admiral Motti thought of the Force - it was only important that Motti had an intense fear of Vader and the Emperor.
The Sith ruled the galaxy by fear and their Imperial officers were held in check by it.
Vader does not care what Imperial Officers believe, only that they are fearful of him and the Emperor to the point of complete submission.
He demonstrates this consistently throughout the trilogy.
It is very similar to the phrase
"The Emperor is not as forgiving as I am."
Whether Vader or the Emperor is the more forgiving person is really not the point.
The point is to remind the officer of his intense fear (of both Vader and the Emperor) in order to keep him motivated in a subservient manner.
scifi.stackexchange.com/users/19815/Richard Venable
Unless I'm mistaken Vader is finding the lack of faith his subordinate has in Vader's abilities to complete the tasks the subordinate outlined.
A complete phrase would sound more like, "I find your lack of faith in my abilities, disturbing."
Something like that.
scifi.stackexchange.com/users/11124/MinimumWageJames
This is the exchange as printed in the script (my emphasis added): MOTTI:
Any attack made by the Rebels against this station would be a useless gesture , no matter what technical data they've obtained.
This station is now the ultimate power in the universe.
I suggest we use it!
VADER:
Don't be too proud of this technological terror you've constructed.
The ability to destroy a planet is insignificant next to the power of the Force.
MOTTI:
Don't try to frighten us with your sorcerer's ways, Lord Vader.
Your sad devotion to that ancient religion has not helped you conjure up the stolen data tapes, or given you clairvoyance enough to find the Rebel's hidden fort...
Suddenly Motti chokes and starts to turn blue under Vader's spell.
VADER: I find your lack of faith disturbing.
Vader was disturbed by two things: Motti's lack of faith in the Force to help Vader fight the Rebels.
Motti's undue faith in the Death Star over the Force.
Motti thought the Death Star cannot be destroyed (obviously Motti would shortly be proven wrong) and that it was the "ultimate power in the universe" instead of the Force (which is blasphemous to Vader, and also incorrect).
As Vader indicated, the Force is still more powerful than the Death Star -- the Force cannot be destroyed and, while the Death Star can destroy a planet, the Empire owed its existence to the (dark side of the) Force.
Vader was disturbed by Motti's overconfidence in the Death Star at the expense of faith in the Force.
scifi.stackexchange.com/users/31936/Null
I find your lack of faith disturbing   -  Darth Vader   What a great Quote! This inspired his own  meme .   But does it make any sense?  Why would the fact that an officer didn't believe in the force disturb Vader in any way? He is not a preacher or a missionary trying to propagate the  Good News of the Dark Side .
Why would Darth Vader find someone's lack of faith (in the power of the Dark Side) disturbing?
scifi.stackexchange.com
<star-wars><darth-vader><the-force>
scifi.stackexchange.com/questions/22827
scifi.stackexchange.com/users/45/DavRob60
Vader was not disturbed, except to the extent that he was annoyed by an obviously ignorant and arrogant officer who dared challenge him.  As would any Sith, Vader took his Dark Side seriously. The officer challenges him which in turn irritates him. He is irritated by the officer; not disturbed.
The officer challenges him which in turn irritates him. He is irritated by the officer; not disturbed.