You should tell her why. Don't hold back on your reasons, she needs to know it all. But, be careful. From the sounds of it, she is going to try to bait you into staying in that situation, maybe even try to have sex with you to prevent you from leaving. Don't fall for it, be strong and know that there are better women out there who will be good to you. Avoid any and all contact from her after you break up with her too, you might think your feelings have calmed down enough to have contact, but that is rarely ever they case.
If you were to just leave and say nothing, then you would be put in an awkward spot one day when you two bump into each other. It always happens.
If she tries to insult you when you inform her, you have a decision to make. Be calm and respectful in your replies back or quip back. Personally, if I wasn't such a quick talker I would rather be calm and respectful but I tend to speak before thinking in cases like that which doesn't end well often honestly. Either way, just leave without dealing with the negativity if it gets to that point.