Trade deficit is short for "trade deficit between Nation A and Nation B." It's a fairly useless concept. Nations, like human beings, don't conduct trade on a purely bilateral basis. Trade is multilateral. That means that while A may have a deficit with B, they can still have a surplus with C or D. If A doesn't have a surplus with anyone (i.e., produces little if anything that anyone else wants), then no trade involving A can even occur. But as long as trade continues to occur, and keeping in mind that trade can only occur if both parties expect to benefit, we have to assume that A's surpluses are more or less equaling A's deficits.
The concept of a deficit in trade between only two nations, then, amounts to a kind of statistical cherry-picking. Deficits would only be a problem if they were absolute (i.e. between Nation A and all other nations) and not merely bilateral.
The whole idea of "parity in trade" as measured according to nations is completely unrealistic and could never be applied consistently in practice. There is no logical reason to think that each other country's value of imports from the U.S. should balance with its exports to the U.S. Some countries have more stuff that Americans want than others. And not all the people in every other country want or can afford a lot of the stuff that Americans make. The point of international trade is not that each and every country will want a certain amount of U.S. exports to offset a certain amount of U.S. imports, but that there will be enough aggregated countries' imports of U.S. exports to offset all U.S. aggregated imports of other countries' exports.
The only way that trade deficits could be a sign of something wrong is if they were funded by government debt. If the U.S. government issues massive amounts of debt in order to fund its deficit-spending, and if this debt is purchased by persons or institutions in foreign countries, and if this debt is then counted as a "trade deficit," then you might claim that trade deficits are bad. But to be accurate, you'd have to say that the real problem isn't the deficit; it's the government debt that enables the deficit.