Why does Graves want to find an Obscurial so badly?

Question

In the Fantastic Beasts and Where to Find Them (2016) movie, why does Graves want to find an Obscurial so badly?

Answer 1

Graves/Grindelwald wanted to find an Obscurial real bad because Grindelwald believes that only an really powerful Obscurial can kill Dumbledore.

I say powerful because Obscurials barely live past 10 years of age. But Credence reaches his 20s which makes him an extremely powerful Obscurial, capable of extreme destruction.

In 'The Crimes of Grindelwald', it is revealed that Grindelwald believes Credence to be the one who can defeat Dumbledore.

KRALL Why is he so important?

GRINDELWALD walks to face KRALL.

GRINDELWALD Who represents the greatest threat to our cause?

KRALL Albus Dumbledore.

GRINDELWALD If I asked you now to go to the school where he is hiding and kill him for me, would you do it for me, Krall? (smiles) Credence is the only entity alive... who can kill him.

KRALL You really think that he can kill the great—can kill Albus Dumbledore?

GRINDELWALD (whispers) I know he can. But will you be with us when that happens, Krall? Will you?

_{Fantastic Beasts: The Crimes of Grindelwald - The Official Screenplay, Scene 46}

So when Grindelwald learns of 'a powerful Obscurial in New York', he goes there to find the Obscurial. Unknowingly that Credence himself is the Obscurial, Grindelwald enlists the help of Credence to find the 'Obscurial'. Once he comes to know that Credence is the Obscurial, he tries to gain his trust which ends up badly for Grindelwald in Part 1 (everyone thinks Credence is dead by part 1 end). Grindelwald then tries to get Credence into his ranks in Paris, so that he can defect Dumbledore using Credence.

Additional Fact:

Why Grindelwald can't go against Dumbledore himself and needs Credence/Obscurial? Because Grindelwald and Dumbledore made a blood-pact to not fight each other. So they can't fight each other even if they wanted to. So Grindelwald wanted to accomplish this using an extremely powerful Obscurial.

Answer 2

Probably because of Ariana Dumbledore.

In Harry Potter and the Deathly Hallows, we learn about Ariana Dumbledore, Albus's sister.
While the term "Obscurus" or "Obscurial" is never mentioned in the original series, the description of an Obscurial matches the description given of Ariana.

JACOB: Can someone please tell me what this Obscurial - Obscurus - thing is? Please?

TINA: There hasn't been one in centuries.

NEWT: I met one in Sudan three months ago. There used to be more of them, but they still exist. Before wizards went underground, when we were still being hunted by Muggles, young wizards and witches sometimes tried to suppress their magic to avoid persecution. Instead of learning to harness or to control their powers, they developed what was called an Obscurus. It's an unstable, uncontrollable Dark force that bursts out an attacks... and then vanishes.
_{Fantastic Beasts and Where to Find Them (2016) (source)}

Aberforth glared at her: His lips moved as if he was chewing the words he was holding back. Then he burst into speech.
"When my sister was six years old, she was attacked, set upon, by three Muggle boys. They'd seen her doing magic, spying through the back garden hedge: She was a kid, she couldn't control it, no witch or wizard can at that age. What they saw scared them, I expect. They forced their way through the hedge, and when she couldn't show them the trick, they got a little carried away trying to stop the little freak doing it."
[...]
"It destroyed her, what they did: She was never right again. She wouldn't use magic, but she couldn't get rid of it; it turned inward and drove her mad, it exploded out of her when she couldn't control it, and at times she was strange and dangerous. But mostly she was sweet and scared and harmless.["]
_{*Harry Potter and the Deathly Hallows, chapter 28: "The Missing Mirror"}

Ariana then ended up dying, during a fight between Albus, Aberforth, and Gellert Grindelwald... who was Albus's closest friend for a long time, and was often at his house.

Gellert was familiar with Ariana and was there when she died. This most likely gave him an inkling of just how powerful and Obscurus was, and perhaps also gave him an urge to prevent more of these cases; after all, he was entirely pro-wizard, and having a wizard die early because of repressing magic - being caused by Muggles - would have been something that Grindelwald would be entirely against. And so we see that Graves - aka Grindelwald in disguise - wanted to save Obscurials - such as Chastity, Credence's sister, who he originally thought was the Obscurial, and Credence himself, once he was revealed to be the Obscurus.