I know this thread has been beaten to death by most on the dangers of sub-ohm vaping. However, I wanted to chime in with an engineer's perspective as to the 'why' it is dangerous to push batteries beyond their capabilities.
The trouble with pulling huge amounts of current through a non-safe chemistry battery (read: every battery you use in a mod) is not necessarily current, but heat. The truth is, Lithium is a highly reactive element, and despite the chemistry of modern batteries we still have to worry about the substrate of batteries deteriorating under heat, and the lithium reacting with its surroundings.
Any battery in the real world has an (usually small) internal resistance. For practical purposes, it's safe to assume that this value is below 0.1 ohms. But if you do the math on a sub-ohm setup, you see where the problem is. Let's take, for example, this great post by djslik:
http://www.e-cigarette-forum.com/fo...ms/462202-how-sub-ohm-vaping-dangerous-3.html
In his example, with a .3 ohm coil, and .05 ohms in both the mod and the battery, he comes up with 10.5 amps in the circuit. If you do the power calcs (P = I^2*R), you find that with that circuit you're putting out roughly 33 W through the atty. However, we also have to consider that you're putting out power INTO THE INTERNAL RESISTANCE OF THE BATTERY. Using djslik's numbers, this power into the battery (as heat) is roughly 5.5 W. Compare this with what someone would call a 'more safe' setup, running only 3A through a 1.3 ohm coil, and the heat into the battery is only .45 W.
So what does that mean? Power, literally, is the rate at which energy is transferred into or out of a system. So, referring to the above examples, with a .3 ohm coil and some assumed numbers on battery resistance, the 'unsafe' setup is pumping heat into the battery at a rate greater than 10 times that of the 'more safe' setup. Food for thought.
Now, the point, which I eluded to earlier. Heat is the killer of batteries. The hotter the battery, the greater the chance there is for the underlying chemistry of lithium batteries to go unstable, and into a condition known as 'thermal runaway.' Basically, the heat allows a chemical reaction inside the batteries, which generates more heat, which causes more reactions, etc etc etc. This is what happened to the 787's which were grounded for battery fires a few months ago, using a battery chemistry which is VERY similar to that which you use on a daily basis to heat up your favorite nic juice.
Reputable battery manufacturers publish specifications for maximum charge and discharge rates of their batteries, along with numerous other data, so that designers can properly utilize their product. The manufacturer more or less guarantees that its batteries will perform safely, as long as they are kept within spec. It is the job of the designer (in this case, the modder) to make sure he stays within those limits.
Whew! Okay, end rant. Hope that sheds a little light on the subject for everyone.