Because in my opinion, and the opinion of thousands and thousands of others the iPhone does not work like it should. It is a great phone but since I paid for it I feel very entitled to have it operate the way I want it to. Apple controls the app store and refuses to let certain customization apps be distributed. Imagine buying a car that wouldn't let you change the radio station or buying a computer that woulnd't let you change the home page. The concept is similar.
Just a few quick examples are:
Messaging... I like to have time stamps so I know what time I sent or received a message. Apple doesn't allow me this option but Xmessages from Cydia (the jailbroken app store) does that. I found Bitesms too buggy but lots of people love it. It has several additional options to include skins. When I get a text I usually can't feel the two short vibes and Apple doesn't give me a way to change this so RingerX Vip from Cydia lets me create my own custom vibes for text and many many other things.
When my phone is on loud and I send a text, I don't want to hear *whoop* and I don't want everyone around me to know I just sent a text but Apple doesn't give me the option to turn it off. iFile from the Cydia store allowed me to delete that .caf file so it will never make that sound again when I send a text even if my phone is one loud.
I hate butt-dialing people and often called them on accident when just viewing their contact info. Asktocall from Cydia allows me to require a confirmation before the phone actually dials someone.
When I miss a call, I want to know about it. With Missed Reminder I can set a reminder (like a text reminder) that I missed a phone call. Apple didn't give me that option.
I don't use themes but my wife does and love it on her JB 4S. Apple doesn't allow themes I don't think.
So why break something that works like it should you ask? It doesn't work like it should- it works like Apple thinks it should work for everyone and I want a phone that works that way I want it to work. And to be clear, you're not actually breaking anything. You're putting your phone into administrator mode which allows you to control your device without restrictions and allows you to use Cydia to download and install the customizations that YOU want- not that Apple thought you should have. Had I not been able to JB my iPhone I was going to go back to Android so I could have all the little customizations that I wanted. It was a painful couple of months waiting for the JB to be released and if it hadn't have come, I wouldn't be here.
Edit Here: To the original poster- no, I have not had ANY issues related specifically to the jailbreak. Some of the apps I've downloaded have been buggy but that's it. I don't believe for a second that simply jailbreaking changes anyone's battery life either. It's related to the apps they download that use more system services, location, push notifications etc. BiteSMS and RingerX VIP are the two buggiest apps I've had. I ditched BiteSMS but love ringer x despite it's shortcomings.