Writing, like every other profession in the world, comes with rules. But the people that seem to succeed at writing, or indeed any creative medium are the ones we label innovators, which is really just a fancy word for rule breaker. It's not as simple as ignoring everything your English teacher ever taught you. Rebellion, when done right, isn't mindless anarchy, it's smart.
The old saying is correct. To break the rules you must first know what they are, and in writing there are two main sets of rules. Hard rules and soft rules. Hard rules are things that are needed to make a piece of writing understood. Basic language rules, spelling, grammar. They also include genre specifications such as horror must be scary and romance must include characters falling for one another. Soft rules are ones that can be played with, carefully. In fact most breaking or bending of soft rules is widely acceptable. Hard rule bending or breaking on the other hand needs a careful hand and a thick skin.
Language, spelling, and grammar contain the hardest of the hard rules. Failure to follow them means we run the risk of not being understood or people thinking we have made mistakes. But even the hard rules of language can be bent.
Most languages of the world are not dead, meaning the constantly evolve and take on new words. Never has this been more evident than in the internet age. I could write a story today, use the word Google as a verb and almost everyone would know what I mean. It's the same with tweet and blog. But before the prolific invention of new words in the internet age there were a few innovators out there constantly bending the rules. One of which was Lewis Carroll. Have you ever read the Jabberwocky? I urge you to do it to see what I mean. He made up words as he went along, but by using words that are emotive of the feelings and images he wanted to portray he largely got away with it. A word like “galumphing” sounds like a joyous almost skipping motion, just heavier footed. It could almost pass as a real word. In fact, thanks to the riotous imagination and quest for nonsense in my grandfather, I never knew this wasn't a real world until I was well into my teens. It did enter the dictionaries after many other writers used it, which technically makes it a real word now.
A lot of words we use today originated with people like Lewis Carrol bending the rules, and not all of them started life in nonsense poems. William Shakespeare came up with many words we use today without batting an eyelid. Despite the love and adoration these writers get making up your own words, unless its a few thrown in for a fantasy or sci-fi race you have come up with, will normally be met with confusion and appeals for an explanation. Tread carefully if this is a rule you wish to break.
There are some soft rules in writing structure too Breaking up a book with chapters may be expected, but a few writers don't use them at all (Terry Pratchett for example). Some stories start at the end and flash back throughout. Some take on multiple points of view, like A Song Of Ice And Fire. In general, not keeping to a chapter by chapter chronological account is not going to raise many eyebrows.
Genre is much easier to rebel against, in fact, it is often applauded. Subverting the tropes of genre is opening up a world of stories with a more diverse cast while still sticking to a formula that people expect. People are going to find it very hard to believe that a story about a blossoming friendship can be marketed as a romance without those friends actually hooking up, but a story about group of people exploring polyamory is a romance. They typical heroes journey has been played out so many times, but it can be turned completely on it's head by a simple shift of perspective I.E. the villain telling the story and believing himself a hero.
Breaking the hard rules of genre is hard. Any hope of bending the rules will often lead readers to believe your work belong to another genre entirely. That doesn't mean you should be unduly hemmed in by genre definers, just be prepared to explain your choices.
In short, rebelling against writing rules can help writing evolve and grow, but it is a slow change. By all means, don't let the rules hold you back, but think carefully about the hows and whys of your own personal rebellion. Who knows? You could be the next innovator.