There can be a number of reasons a faucet cartridge leaks after you have installed a new one. It all depends on the age of the faucet, the type of cartridge and water quality.
Many times the reason a faucet leaks has nothing to do with the cartridge. When water (one of the most corrosive liquids we have) runs through a brass body, the water is full of calcium and minerals in solution. This will eat away at small imperfections in the brass in the original casting process. Soft spots in the brass and small bumps can cause the water to remove the brass and form small rivulets in the surface. These are almost impossible to see with the naked eye because it blends in with the coatings left on the surface of the brass from the water. In order to fix a leaky faucet cartridge, I will often have to take a small buffer and buff the inside of the cartridge cylinder to see the line. Since the line is below the surface of the cylinder, the dark matter is left in the line and it shows up as a dark line. You have to use a flashlight to find them.
Other times there is a rubber, brass or ceramic seat in the bottom of the cartridge opening, which is actually forming the seal. These parts can become damaged by the movement of the cartridge as it opens and closes. The brass and rubber can no longer fit properly into the hole in the cartridge cylinder and it can leak. The O-ring that the cartridge rests against can have small cracks and deviations which can a leaky or dripping faucet. When you replace parts in a faucet, generally you will have to replace all of the inside parts. In the cartridge packet should be a list of additional parts that may be necessary to complete your faucet repair and create a complete seal.