All faucets come apart. If you are having trouble pick up a book by Black and Decker on home plumbing repair. It will take you step by step through the proceedure to remove the parts. Make sure you turn off the water to the house. Of course the other option is to get a professional in to help you. But do not give up just yet. Read the book first.
It is a little easier if I know what brand of faucet it is, since there are about 50 manufacturers of faucets and over 5,000 brands. Since you say its a pull out handle, I'm gonna guess its a Moen. The one thing about a moen cartridge faucet is, there is a little clip hidden in the barrel that you have to remove first, before the cartridge will slide out. It looks like a brass horse shoe. Its typically sticking out just a little bit down before the wall plate. You can't see it unless you remove the barrel chrome cover. Thats a sleeve that slides over the barrel and slipps into the wall plate. If you get the clip out, the cartridge has to be turned completely (not just the handle) to be removed. Due to calcium deposits, the o-rings are often stuck to the inside of the barrel.