Money isn't considered capital because money merely facilitates trade and doesn't hold intrinsic value. Capital holds value because it is productive; for example, a tractor is a capital good because it plows fields. A field cannot be plowed with a $5 bill, so money itself cannot be used for productive means.
Calling something "capital" indicates that it is a means of production. A dentist's means of production is a drill, and a carpenter's means of production is a hammer. A carpenter would use money to purchase a hammer, but he wouldn't use money as a direct means of production.
Money can be thought of as a measure of a capital good. Capital goods that hold more productive value ought to cost more money, and conversely, goods that hold less value cost less.
Scarcity drives value in capitalism. If an entire town had one hammer, the hammer would have a high price tag. Money, or rather the cotton and paper used to produce money, isn't scarce. Government treasuries can print money at will and only do so in order to stimulate or reign in economies. Money's value is tied to the amount of goods or services it represents. When the United States used the gold standard, a dollar was worth an exact amount of gold held by the government. The U.S. dollar eventually became purely a symbol of trade.