From what I understand, lightning occurs when frozen water particles in a cloud bump into each other, building up electrical charges. Therefore, wouldn't it make more sense for waterbenders to be able to create lightning strikes? Obviously they gave the firebenders this ability because they are the villains of the show for the most part and they needed a frightening ability to keep tension high, but if it was "logical", then the waterbenders should have this ability, right? If we go even further, only the avatar should be able to create lightning strikes using a combination of airbending and waterbending.
I'm going to tackle this from the angle of what fire and lightning are made of, followed by a quote from the show to try and back me up.
Fire is an oxidizing chemical reaction that releases heat and light. The actual flames that you see moving and glowing when something is burning are simply gas that is still reacting and giving off light.
When lightning strikes, the electric current which passes through the air heats up the air molecules so much they form a plasma, the fourth state of matter. This is because it ionizes the air molecules (they're so energetic the electrons are no longer strictly bound to the nucleus of the atoms inside it).
Now, if you managed to get a flame hot enough, it would change state from a gas to a plasma, as the extra energy from the heat overcomes the electric attraction between the negative electrons and positive nuclei of the atoms in the air. A quote from Iroh to Zuko seems to support this when he says
"There is energy all around us. The energy is both yin and yang; positive energy and negative energy. Only a select few firebenders can separate these energies."
I know he's probably referencing the internal balance of the firebender (since only those with inner peace can perform the art), but I think it's also a nod from the mystic to the scientific. As a further point, firebenders draw energy from the sun, which itself is so hot most of the gasses inside it are in the state of a plasma.
Now as to why waterbenders, or an Avatar with air and waterbending can't do this, I'd say it's simply because it would require an extraordinary level of control of the matter involved to produce the conditions of natural lighting with those forms of bending. Simply put, it's easier to make fire hotter as a firebender, even if it is a tricky skill to master.
If we try to stick with normal physics, the idea of firebenders creating flame from nothing is seriously problematic.
In a real fire, what you see as flame is the boundary where the combustible gas being released by the fuel source reaches the proper mixture with the ambient oxygen for a oxidation reaction to take place. (Almost any fire you'll ever see involves combustible gasses as the final fuel; solid fuels just decompose from heat and release the gasses that ultimately combust.)
So... what? Are firebenders creating combustible gasses out of the surrounding ambient air? If so, they must be rearranging matter on a molecular level, in defiance of conservation of energy. And if they can do that, lightning is easy: command the electrons to go thataway.
Which means there are probably a thousand other things they could do. Create food from base elements, for example. Refine aluminum. Strip the phosphorous out of your ATP and kill you instantly. The possibilities are endless!
Nobody tell them.