"Never turned off a laptop for a few weeks"....what do you mean by this. That people should turn off their computers on occasion?
I'm not sure what he meant by that. It would be irresponsible to leave the laptop running 24/7 though. I can tell you that laptop battery requires a recalibration every once in a while. Once a month is what they recommend.
You can't really leave a laptop on for weeks at a time unless it's plugged in. Not using the battery for weeks isn't recommended by many. The battery itself need to be used at least a few times a week to keep the electrons moving around.
The batteries are supposed to last you for years if used properly. However, a lot of people don't, which is why you see a lot of batteries being replaced within the first couple years.