I'm constantly ridiculing friends and coworkers over the fact that their iPhone doesn't support multitasking. Can you adequately keep an instant messaging application consistently "on" with the iPhone? No, at least not easily. Yet even though I'll callously joke about it, I do agree with Apple's business decision on locking out the feature.
On a purely technical level, allowing the iPhone to support multitasking means the possibility of applications being "on" all the time. Poorly developed apps with memory leaks will consume the phone's memory after prolonged usage, causing the OS itself to become unstable and the phones to be unreliable. The app store fuels this problem in that a lot of the popular apps are not built by Apple.
By supporting multitasking, there is a high degree of risk for these phones to crash unless adequate quality assurance is made. What happens without it? When a phone is mysteriously restarting, will a normal cell phone user understand that the third-party app is the source of the problem? Or will these users just immediately blame Apple for a faulty product?
In terms of branding, Apple's products have never been about being a highly-configurable, feature-rich workhorse. Their products have constantly been revered as devices that "just work". What does this entail? A reliable product that doesn't crash.