My girlfriend says that Rome fell because their plumbing was made of lead and it caused brain damage to the Roman citizens.  I said it was because the Roman Empire became overextended and they couldn't support the long supply lines to their armies.  Who is right?
Neither of you is entirely right or entirely wrong. The fall of the Roman Empire was a complex and multi-faceted event, and there is no single cause that can be said to be the "reason" for its decline.

Lead poisoning from the widespread use of lead plumbing and other lead-based products has been suggested as a factor in the decline of the Roman Empire, as lead exposure can lead to a range of health problems including brain damage. However, this is just one of many factors that likely contributed to the decline of the empire.

At the same time, the overextension of the Roman Empire, along with the associated challenges of maintaining long supply lines and supporting large armies, also likely played a role in its eventual downfall. Additionally, other factors such as economic instability, political corruption, and military invasions also likely contributed to the decline of the Roman Empire.

In conclusion, it is unlikely that any single factor was the sole cause of the fall of the Roman Empire. Instead, it was likely a combination of many different factors that contributed to its decline and eventual collapse.