Some people call it that, but the actual power is "among the several states".
First, Congess must decide to regulate some interstate commerce. Just because wheat, let's say, is interstate commerce, and Congress has the power to regulate interstate commerce, doesn't mean that Congress must regulate wheat.
But let's say that there's a temporary glut of wheat on the world market. American farmers are going bankrupt because it costs more to grow the wheat that what they'll get for it.
Congress decides to regulate the wheat and limit the production in order to raise the price. They guarantee the farmers a set price if they only grow so many acres. The farmers agree. All but one.
This guy decides he'll grow his allotment at the guaranteed price, but then grows a little more for his own use (for bread, animal feed, etc.).
Should he be allowed to do that? Certainly if he can, then you must allow the other farmers to do the same.
Now, if these farmers are growing their own "personal use" amount of wheat, doesn't that have a cumulative affect on demand (ie., they're not buying it in the open market)?
Wouldn't you say that has an effect, perhaps a substantial effect, on interstate trade?
"3d. To "regulate commerce with foreign nations, and among the States, and with the Indian tribes." To erect a bank, and to regulate commerce, are very different acts. He who erects a bank creates a subject of commerce in its bills; so does he who makes a bushel of wheat, or digs a dollar out of the mines; yet neither of these persons regulates commerce thereby. To make a thing which may be bought and sold is not to prescribe regulations for buying and selling. Besides, if this was an exercise of the power of regulating commerce, it would be void, as extending as much to the internal commerce of every State, as to its external. For the power given to Congress by the Constitution does not extend to the internal regulation of the commerce of a State (that is to say of the commerce between citizen and citizen), which remains exclusively with its own legislature; but to its external commerce only, that is to say, its commerce with another State, or with foreign nations, or with the Indian tribes. Accordinglythe bill does not propose the measure as a regulation of trade, but as "productive of considerable advantages to trade." Still less are these powers covered by any other of the special enumeration. " - Thomas Jefferson, on establishing a national bank.
Jefferson says if Congress cannot regulate an activity in interstate commerce without also regulating intrastate commerce, then it may regulate neither. You say if Congress cannot regulate an activity in interstate commerce without also regulating intrastate commerece, then they may regulate both. One of you is wrong.
But no, I don't believe that growing a little extra for personal use would have any discernable effect on market pricing on a national level. And I certainly don't expect the Fed's to knock on my door for having a personal garden (ie. not farming) that I wish to grow some wheat (or any other crop). Their deal may have been with farmers of wheat, corn, tomatoes, peppers, or whatever else, but that should certainly have no bearing on my backyard garden.