Have you ever maybe neglected to see the dentist for awhile, like ten years, and then one day you wake up and your cheek is swollen and red and your tooth feels like its jackhammering inside your head? All you can think of is WHAT possibly could have caused this pain, and how soon can a dentist get you in to be seen?
So you show up to the dental office, and an x-ray is taken. The dentist comes in and tells you that there is a huge cavity which has made its way down to the nerve of the tooth, and that's the source of your pain and infection (and swelling). And you think, "I brush my teeth twice a day! How could I have that big of a cavity?"
Do you floss? Drink a lot of sugary drinks? Eat candy? Eat carbs? Did you know that carbohydrates eventually break down into sugar, which, exactly the same as real sugar in candy, sits on your teeth and decays them? Even natural sugars found in fruits can cause cavities. Some brands of bottled water have a high pH level, making them acidic, causing acid erosion and weakness on your teeth.
Coming to the dentist every 6 months won't guarantee that you don't get cavities - that's on you to take care of at home. However, x-rays taken every twelve months can detect cavities when they're small, before they reach the nerve of your tooth. Having them filled in a timely manner can save you from the pain and expense of a root canal. Having your teeth cleaned every 6 months helps prevent plaque and tartar (hardened plaque that cannot be removed at home) from building up and allowing bacteria to sit on the teeth.
If you're worried about the cost of seeing the dentist every 6 months, talk to your hygienist before having the cleaning done. Typically insurance covers you based on units of scaling. If you have, for example, 12 scaling units covered per year, and you typically get 3 units of scaling per appointment, you could have your teeth cleaned 4 times in one year. Keep in mind that cleaning does not equal x-rays and checkup. Those are recommended once a year (usually). Perhaps at those appointments you could request no polishing or fluoride if you're still concerned about cost. Talking to your hygienist or dentist about any financial restraints will save everybody in the long run.