Here's why:
* Brake Master Cylinder Failure: The master cylinder is the heart of the hydraulic braking system. It converts pedal pressure into hydraulic pressure to actuate the wheel cylinders/calipers. If the master cylinder seals fail, brake fluid (which is often mistaken for oil due to its similar appearance) will leak out, resulting in a complete loss of braking pressure. This is the most probable cause given the symptoms.
* Brake Lines/Hoses: While less likely to cause a simultaneous loss of *all* braking pressure and oil leak at the pedal, a significant rupture or leak in a brake line or hose *could* do so. However, this would usually manifest as a leak somewhere *under* the car, not directly at the pedal.
* Wheel Cylinders/Calipers (less likely): These components are at the wheels. While a catastrophic failure *could* lead to loss of braking, it's far less likely to result in a leak directly at the brake pedal. Leakage would be at the wheel. A massive leak at all four could theoretically lead to loss of pressure in the master cylinder, but this is improbable.
* Power Brake Booster (less likely): While a faulty power brake booster *could* contribute to reduced braking power, it's unlikely to directly cause a brake fluid leak at the pedal. They usually fail by allowing a vacuum leak or failing completely.
In short: The most probable cause is a failed brake master cylinder seal. The oil is actually brake fluid, and its presence at the pedal is a direct indication of an internal breach in the master cylinder. This is a serious safety hazard, and the car should absolutely *not* be driven until the problem is addressed by a qualified mechanic.