The answers all point out, correctly, that Linux cannot cause the battery to explode, since the charging mechanism is OS-independent. However, it is possible that running Linux could shorten battery life, in both senses. The Linux kernel is less optimized to conserve power than OS X, thus reducing the running time per charge. Over the long term, that additional energy usage could also degrade the battery capacity.
To be fair, Apple does put engineering effort into making its hardware run best with Mac OS X. It is possible, in some cases, that running Linux can strain your hardware more. For example, it could park hard disk heads after excessively short idle periods, leading to premature wear. As another example, the System Management Controller, which governs the fan, is controllable by the OS, so it is remotely conceivable that poor fan control could cause heat-related reliability problems. (Note that fan control hacks exist for OS X, so you don't even need to run Linux to override the fan's behaviour.) Running Linux may strain your hardware, but I wouldn't say that it "damages" it.1
In some sense, your dad is right, in that Apple guarantees only that Mac OS X will run properly on your hardware, for the duration of the warranty period plus whatever AppleCare you bought.2 Apple reserves the right to dismiss any complaints you may have if you're running Linux or even Windows, though the treatment you actually get depends largely on which Apple technician you encounter. And, of course, Debian disclaims all liability. However, I wouldn't let these fears deter you from installing Linux. It is, after all, your machine, so you should enjoy it fully by running your operating system(s) of choice, and chances are that everything will be just fine.
If you really are scared of running a non-Apple-approved operating system, you do have the option of running Linux in a virtual machine within Mac OS X. Then you would be technically abiding by Apple's rulebook while getting a Linux-like experience.
1 Except when it does, in extremely weird situations that will never apply to you.
2 A similar argument could be made for, say, how Acer only supports Windows. Unless the manufacturer has certified their machine to run Linux, you assume any risk. Canonical has a certified hardware list for Ubuntu; Debian only has a hardware compatibility list.