Why is the unit for capacitance so large?

Because it fits in with all the other (SI) units we have. 1 farad is 1 coulomb per volt. It just so happens that 1 coulomb is... a lot of charge.

Because 1 Ampere is a unit so large compared to the amount of current we normally use. Because 1 second is a unit so large compared to the audio and rf frequencies we normally use.

If you normally use currents much smaller than 1A, for periods much shorter than 1sec, and don't have a lot of money to waste or a lot of space to waste, you can use capacitors much smaller than 1F.

On the other hand, if you wanted to do electrical power, instead of radio electronics, 1F isn't very big. Here is a recent press release on a 400F capacitor. http://www.engineering.com/ElectronicsDesign/ElectronicsDesignArticles/ArticleID/5290/Is-it-a-battery-No-its-a-Supercap.aspx -- and note that the special feature is that it is no larger than a deck of cards.

As others have mentioned, 1 farad is 1 coulomb per 1 volt. But the rabbit hole goes deeper -- the question then becomes why is 1 coulomb what it is, and why is 1 volt what it is?

Following this rabbit hole to the bottom will eventually lead us to the 7 base SI units, which are units of measure for the 7 physical attributes of our world: distance, mass, time, electric current, thermodynamic temperature, amount of a substance, and luminar intensity. They're like axioms in mathematics. From here, other units are defined in terms of these. So volt = (kilogram meter meter) / (ampere second second second). Meanwhile coulomb = ampere * second. You'll notice that 1 of a derived unit is expressed in terms of 1's of a base units.

So ultimately, 1 farad is so large because the base units are so large, at least relative to the sizes of electronic components nowadays where we fit billions of transistors onto several square millimeters.