We see in the Harry Potter universe, wizards or witches keep obliviating Muggles/No-Majs, because otherwise it may lead to chaos or persecution of witches/wizards.

However, the Dursley family cannot be obliviated since they have to give Lily's protection to Harry. Obviously they did not like Harry, so why did they not expose the magic world?

Why would they do it?

As you said, they hate Harry. They want to be away from him as much as possible, and all he represents (i.e., Wizardry). The Dursleys want to be normal above all else. They want to be regarded as successful, but anything crazy sounding is a big no-no for them.

Mr and Mrs Dursley, of number four, Privet Drive, were proud to say that they were perfectly normal, thank you very much.

They live much better by ignoring Harry and pretending he doesn't exist at all.

The Dursleys had everything they wanted, but they also had a secret, and their greatest fear was that somebody would discover [...] about the Potters.

Also, who would believe them if they said Wizards existed? No one. Child protective services would arrive much sooner than a squad of scientists to study poor Harry.

The Dursleys don’t want people knowing.

The Dursleys would never want to expose magic to the world, because they never wanted anyone to find out about their unusual relatives. They were afraid of that happening, and intensely wanted to avoid it.

“The Dursleys had everything they wanted, but they also had a secret, and their greatest fear was that somebody would discover it. They didn’t think they could bear it if anyone found out about the Potters. Mrs Potter was Mrs Dursley’s sister, but they hadn’t met for several years; in fact, Mrs Dursley pretended she didn’t have a sister, because her sister and her good-for-nothing husband were as unDursleyish as it was possible to be. The Dursleys shuddered to think what the neighbours would say if the Potters arrived in the street.”
_{^{- Harry Potter and the Philosopher's Stone, Chapter 1 (The Boy Who Lived)}}

They certainly wouldn’t reveal that secret by telling people that magic exists and they know about it themselves. They took pride in their normalcy, and wouldn’t want to be known as being involved in anything so unusual and abnormal as wizards and magic.

“Mr and Mrs Dursley, of number four, Privet Drive, were proud to say that they were perfectly normal, thank you very much. They were the last people you’d expect to be involved in anything strange or mysterious, because they just didn’t hold with such nonsense.”
_{^{- Harry Potter and the Philosopher's Stone, Chapter 1 (The Boy Who Lived)}}

Telling people magic exists would be the exact opposite of what the Dursleys would want to do - they wanted it, and more importantly their tangential involvement with it, to stay secret.

1. They have no motive. It wouldn't benefit them, other than spite, and although it wouldn't be out of character for them to act out of spite, they seem to be more wanting to ignore the wizarding world than harm it.




2. They are living in denial. For the first ~10 years of Harry's residence, they simply pretended that magic didn't exist, and after he started attending Hogwarts, they tried as best they could to continue doing so.




3. They don't have much in the way of proof. The wizarding world isn't going to do magic in front of them while they're holding a camcorder, and even if they got proof, the wizarding world likely could get rid of it. That just leaves the Dursleys ranting like crazy people about wizards and witches.




4. They know little about the magic world. When Harry first comes home from Hogwarts, they are afraid around him, worried about what magic he can do, until they find out that he'll get in trouble if he does magic outside of school. Clearly, no one's going out their way to explain everything to them. Maybe they can't be obliviated, but they don't know that, nor do they know whether there's anything else can be done to them.

If I'm not mistaken, in the "Harry Potter" books it was made clear that the Dursleys despised everything out of ordinary and one of their main aspirations in life was to be perfectly normal. So they would definitely not want to do something as eccentric, as saying that wizards and witches exist.