Remus is old enough to be her father. Seeing as he is the same age as Harry's parents and Harry is a year younger than Hermione. If we ignore the age difference because apparently teacher/student relationships aren't squicky in the Wizarding World, or perhaps they're out of school or time travel is involved or SOMETHING relevant has occured...
Remus is on the Light side, a bookworm, prefect, Gryffindor and is close to Harry. These are about the only things he has in common with Hermione. In point of fact, he accepts his lot in life and doesn't attempt to fight for the rights of werewolves. However Hermione is always up in arms about S.P.E.W or muggleborn rights, or how it's totally barbaric to do any number of Wizarding things.
Now. Going off what we know of Hermione, she's had a schoolgirl crush on Gilderoy Lockhart, so we know she's somewhat shallow when it comes to what she wants in a man. Lupin in that regard is somewhat greying, balding and scarred from his stressful life as a werewolf, poor man. Anything beyond that where Hermione's interests are concerned are merely psycho babble and speculation, (due to the train-wreck of the Hermione/Ron 'ship) but what we do know is that she is attracted to beauty and/or idiocy. Neither of which Lupin portrays. Yet Krum did. And Ron did too, in eye-bleeding amounts. Also while figuring out that he is a werewolf we learn that she is intuitive to his secrets, of which he has many as we know very little of his life prior to the series and during it, for that matter. As a private person, one would think that Remus would not want people to pry into his personal life. He did not seem particularly happy that Hermione, a thirteen year old witch, figured him out after a few months (when Snape set the essay).
Going from what little we know of Lupin, he is a caring father, a family friend, a best friend and an excellent professor, though he did focus mostly on dangerous magical "Dark" creatures (as did Hagrid for that matter...) and not so much on spells. He is virtually penniless, a charity case of Dumbledore's, has no real qualifications due to being a werewolf, he's intelligent and quick thinking, loyal to a fault and follows rules - which we know Hermione does not.
Once one sands down this 'ship to it's bare boards, it shows this: These two are not compatible, but somebody, somewhere, thinks that having all one's Dark secrets ferreted out by somebody who is young enough to be one's daughter, is plausible grounds for a relationship... are you high?