The most obvious reason is cost, it can be considerably cheaper for you to Repair your PSP rather than send it away to be fixed, unless it is under warranty anyway. A Playstation Portable console is not a cheap item to purchase, so the last thing you want to be doing is either sending it away for costly repairs of even purchasing a new PSP because your current one is faulty.

There are many console repair companies on the internet and obviously Sony themselves but there is no reason why most repairs can not be done by yourself at home in your spare time.

Now it is not for everyone, not to say that you need a massive amount of technical knowledge but some of the repairs can become quite complicated, ie, motherboard issue or replacing a UMD drive. It is okay taking a PSP apart but you need to be able to put it back together again, you need to keep track of which screws go where and that all you connector cables/ribbons are connected, but it is all possible with a little bit of time and patience.

In most cases you can get all the replacement parts you need of the internet and cheaply too, especially from Ebay. If you are in any doubt about fixing a PSP console youself then ofcourse let a professional look at it for you, but otherwise give it go and if you find you can fix the problem yourself you will find it extremley rewarding whilst also saving a bit of money in the process.