I'm the programmer
is a correct assumption only if you're the only programmer.
In many cases, other programmers work with the first programmer's code. They use it in ways he didn't intend by fiddling with the values of fields they shouldn't, and they create a hack that works, but breaks when the producer of the original code changes it.
OOP is about creating libraries with well-defined contracts. If all your variables are public and accessible to others, then the "contract" theoretically includes every field in the object (and its sub-objects), so it becomes much harder to build a new, different implementation that still honors the original contract.
Also, the more "moving parts" of your object are exposed, the easier it is for a user of your class to manipulate it incorrectly.
You probably don't need this, but here's an example I consider amusing:
Say you sell a car with no hood over the engine compartment. Come nighttime, the driver turns on the lights. He gets to his destination, gets out of the car and then remembers he left the light on. He's too lazy to unlock the car's door, so he pulls the wire to the lights out from where it's attached to the battery. This works fine - the light is out. However, because he didn't use the intended mechanism, he finds himself with a problem next time he's driving in the dark.
Living in the USA (go ahead, downvote me!), he refuses to take responsibility for his incorrect use of the car's innards, and sues you, the manufacturer for creating a product that's unsafe to drive in the dark because the lights can't be reliably turned on after having been turned off.
This is why all cars have hoods over their engine compartments :)
A more serious example: You create a Fraction
class, with a numerator and denominator field and a bunch of methods to manipulate fractions. Your constructor doesn't let its caller create a fraction with a 0 denominator, but since your fields are public, it's easy for a user to set the denominator of an existing (valid) fraction to 0, and hilarity ensues.