Chemistry - Why isn't ethane used for cooking?
Solution 1:
Probably the biggest drivers behind using methane as a fuel is that it is abundant in natural gas and is (currently) mostly useless as a chemical feedstock. Ethane makes up a few percent of natural gas and can also be obtained as byproducts of petroleum refining, but the big difference from methane is that ethane is extremely useful in chemical synthesis (mostly to make polyethylene). In fact, household natural gas often contains a bit of ethane, which may vary depending on the current demand for ethane as a feedstock. In short: it burns just as well, but ethane has other important uses.
Propane has some use as a feedstock, but it is an attractive fuel because it is easily stored as a liquid without requiring huge pressures.
Solution 2:
In both cases, there appears to be a confusion of terminology between common and technical uses.
We commonly use methane and propane for cooking (and home heating), but not ethane. I would expect ethane to be suitable for this, being in between the two, but I've never heard of anyone using it for this purpose. Why is that?
In reality, anyone using natural gas as a cooking fuel likely is cooking both with $\ce{CH4}$ and $\ce{C2H6}$. From the above-linked Wikipedia page (emphasis added):
Natural gas is a naturally occurring hydrocarbon gas mixture consisting primarily of methane, but commonly including varying amounts of other higher alkanes, and sometimes a small percentage of carbon dioxide, nitrogen, hydrogen sulfide, or helium.
EngineeringToolbox.com reports the following representative composition ranges (probably in percent by volume?) of natural gas:
$$ \text{Composition (%)} \\ \begin{array}{cccccccccc} \hline & \ce{CO2} & \ce{CO} & \ce{CH4} & \ce{C2H6} & \ce{H2} & \ce{H2S} & \ce{O2} & \ce{N2} \\ \hline \text{Min} & 0 & 0 & 82 & 0 & 0 & 0 & 0 & 0.5 \\ \text{Max} & 0.8 & 0.45 & 93 & 15.8 & 1.8 & 0.18 & 0.35 & 8.4\\ \hline \end{array} $$
Given that $\ce{CH4}$ is by far the major constituent of natural gas, it is sensible that it is referred to commonly by the term methane, even if it is often actually a mixture of methane, ethane, and trace higher hydrocarbons.
On a related note, why is butane used for cigarette lighters and basically nothing else (in ordinary life, I mean)?
Per the Wikipedia page for liquefied petroleum gas, linked in Mithoron's comment, most of what is commonly referred to as propane or butane is actually a mix of $\ce{C3H8}$ and $\ce{C4H10}$ in varying ratios (emphasis added):
Liquefied petroleum gas or liquid petroleum gas (LPG or LP gas), also referred to as simply propane or butane, are flammable mixtures of hydrocarbon gases used as fuel in heating appliances, cooking equipment, and vehicles. ... Varieties of LPG bought and sold include mixes that are mostly propane ($\ce{C3H8}$), mostly butane ($\ce{C4H10}$) and, most commonly, mixes including both propane and butane. In the northern hemisphere winter, the mixes contain more propane, while in summer, they contain more butane.
So, Mithoron is right: $\ce{C4H10}$ is used in much more than just cigarette lighters, it's just that common usage happens to apply the term butane for this context.
As a further note, I would guess the primary rationale for using different mixes of $\ce{C3H8}$/$\ce{C4H10}$ deals with the vapor pressures of the two gases. The energy densities $\eta$ of the liquefied gases, approximated as $-\Delta H_c^\circ\rho \over \mathrm{MW}$, are nearly equal:
$$ \begin{array}{ccccc} \hline \text{Quantity} & \text{Units} & \ce{C3H8} & n\text{-}\ce{C4H10} & iso\text{-}\ce{C4H10} \\ \hline \Delta H_c^\circ & \mathrm{kJ\over mol} & -2202^1 & -2878^2 & -2869^3\\ \mathrm{MW} & \mathrm{g\over mol} & 44 & 58 & 58 \\ \rho & \mathrm{g\over mL} & 0.58^4 & 0.604^5 & 0.56^6 \\ \hline \eta & \mathrm{MJ\over L} & 29.0 & 30.0 & 27.7 \\ \hline \end{array} $$
Thus, roughly comparable energy value is obtained per volume of each, and there is little reason to favor one or the other on this basis.
Practically, the lower limit of acceptable vapor pressure is that which provides sufficient flow of gaseous hydrocarbon to the point of combustion. The upper limit is more or less defined by the strength of the container and plumbing. Consider the following vapor pressure data, calculated from fitted equations (sources: propane | n-butane | iso-butane):
$$ \text{Vapor Pressure (atm)} \\ \begin{array}{ccc} \hline & 0~^\circ\mathrm C& 25~^\circ\mathrm C & 38~^\circ\mathrm C \\ \hline \ce{C3H8} & 4.7 & 9.3 & 12.8 \\ n\text{-}\ce{C4H10} & 1.0 & 2.4 & 3.5 \\ iso\text{-}\ce{C4H10} & 1.5 & 3.4 & 4.9 \\ \hline \end{array} $$
Cigarette lighters (especially disposable plastic ones) presumably do actually use butane-rich fuel mixes, so as not to approach or exceed the mechanical limits of the lightweight, portable containers. As well, the temperature at point-of-use is somewhat better controlled, as even on cold days the heat from the user's hand is likely to maintain the butane vapor pressure high enough to provide sufficient gas flow. Finally, as noted in a comment by A.K., lighters are generally charged with iso-butane, which is sensible as it is the isomer exhibiting modestly higher vapor pressures.
For applications where metal-walled containers are feasible (grilling, automotive fuel, etc.), however, structural considerations are less important and the higher deliverable pressure from propane becomes advantageous. In hot summer months, though, I would assume the higher fraction of butane is used so as to mitigate the fairly dramatic increase in vapor pressure of pure propane with increasing temperature.
$^1$ Wikipedia, "Propane (data page)"
$^2$ Wikipedia, "Butane (data page)"
$^3$ Wikipedia, "Isobutane (data page)"
$^4$ Engineering Toolbox, "Chemical, Physical and Thermal Properties of Propane Gas - $\ce{C3H8}$
$^5$ Engineering Toolbox, "Chemical, Physical and Thermal Properties of n-Butane"
$^6$ AeroPres, "Physical Properties" datasheet (PDF link)