Disclaimer: I do not say Jane Austen is a bad, overrated writer, only, I personally don't like her, and am about to explain why. And when I say I don't like Jane Austen, what I refer to is not her as a person, but her writing, her books, her world.
1/ I don't like the way she characterises her characters. We see them, know about them, understand them not through their actions, but mostly through what Jane Austen says about them and what other characters say about them and what they say about themselves. Thus they aren't as real and full of life as characters created by Lev Tolstoy, Fyodor Dostoyevsky, Charlotte Bronte, Emily Bronte, Charles Dickens...
2/ I prefer complex, multi-faceted characters.*
3/ I don't like the world she describes and, more importantly, the people in it (whether she likes them or means to mock them, make fun of them). The people of the gentry class, idle and inquisitive and petty and rude and dull, who have nothing to do but go from house to house, party to party, ball to ball, discussing all other people, poking their noses into others' businesses (more outrageously, they even read letters addressed to somebody else). People of trivial interests and concerns, such as who's interested in whom, who suits whom, who's engaged to whom, who wants to get married, etc. They don't even talk of other topics like literature, philosophy, social problems, gender issues, injustice, the meaning of existence... As Ralph Waldo Emerson puts it, "Her characters live in such a wretchedly narrow view of life that suicide would be more respectable."
I reckon people praise her for depicting that world honestly and vividly, but I find her characters tedious and odious.
4/ I prefer books that are thought-provoking and haunting, and it's even better if they, in a way, torment me. Or, like Kafka puts it, "I think we ought to read only the kind of books that wound or stab us. If the book we're reading doesn't wake us up with a blow to the head, what are we reading for? So that it will make us happy, as you write? Good Lord, we would be happy precisely if we had no books, and the kind of books that make us happy are the kind we could write ourselves if we had to. But we need books that affect us like a disaster, that grieve us deeply, like the death of someone we loved more than ourselves, like being banished into forests far from everyone, like a suicide. A book must be the axe for the frozen sea within us. That is my belief." I love Lev Tolstoy, Fyodor Dostoyevsky, F. Scott Fitzgerald, Toni Morrison, Franz Kafka, George Orwell, Vladimir Nabokov... Jane Austen's novels don't make me think and don't teach me anything.
5/ Her novels are light and predictable. Take "Emma" for instance, right from the beginning I knew that Emma Woodhouse and George Knightley would end up with each other, and I was right. The same goes for Elizabeth Bennet and Mr Darcy in "Pride and prejudice".
6/ She's the mother of chicklit. I don't like chicklit.
7/ (This final point is added after I read several debates revolving around Jane Austen) I know how popular she is and perfectly understand why. As written above, I don't call her a bad writer. Yet I find her books unbearable, and it gets on my nerves to see all the girls who worship her react strongly when somebody attacks Jane Austen, and say that person simply doesn't get Jane Austen or isn't mature enough to see the depth of her books. It gets on my nerves.
*: Please do not refute this point by comparing Jane Austen to Stephenie Meyer, which I have seen lots of people do.