Others have addressed the economic and social aspects fairly well, so I won't repeat them except to throw in a Trump quote which sums it up:
"A nation without borders is not a nation."
Anyone who agrees with this sentiment, and likes their country and wants to preserve it, would therefore want "borders" in a meaningful sense. And even your question implies that globalization and "borders" are somewhat opposed concerns.
Moving on, the third argument against globalization (complementing economic and social) is governmental. Up until this point in civilization on earth, no single Power has governed the entire world. While a tyranny may exist in one place, prosperity may exist in another. Genocide here, peace there. And it has often happened in history that the power of a tyrant, or a corrupt state, is checked or overthrown by another sovereign state. (Think North and South Korea, Nazi Germany, etc.)
Ancient Rome I think is an instructive example of this argument. The empire had a really long run. At its peak, to travel from Rome itself to a place not ruled by it would take weeks or months. And Rome was ruled for hundreds of years by a series of debauched tyrant Emperors, each seemingly worse than the last, punctuated by only a few "good" ones. This continued until finally the corruption of Rome was so complete that the capital city became vulnerable to outside threat.
But what happens if a single power dominates the world, and becomes a tyranny or a genocidal state, with no outside equal to check it?
George Orwell envisioned in 1984 a world governed jointly by three more or less cooperating super-powers who use a false, perpetual war between them to "use up the products of the machine without raising the general standard of living"; who control all communication, historical records, education, and thereby remove even the will of people to rebel against them; who dominate and enslave all humanity. Of course, 1984 is a work of fiction, but it is mentioned with interesting frequency in the American media of all political stripes.
The Internet seems to confirm that the late influential billionaire David Rockefeller wrote this in his autobiography:
For more than a century ideological extremists at either end of the political spectrum have seized upon well-publicized incidents such as my encounter with Castro to attack the Rockefeller family for the inordinate influence they claim we wield over American political and economic institutions. Some even believe we are part of a secret cabal working against the best interests of the United States, characterizing my family and me as ‘internationalists’ and of conspiring with others around the world to build a more integrated global political and economic structure — one world, if you will. If that's the charge, I stand guilty, and I am proud of it.
And he is rumored, but it appears not proven, to have said this as well in private:
We are grateful to the Washington Post, The New York Times, Time Magazine and other publications whose directors have attended our meetings and respected their promises of discretion for almost forty years. It would have been impossible for us to develop our plan for the world if we had been subject to the bright lights of publicity during those years. But the world is now more sophisticated and prepared to march toward a world government.... The supranational sovereignty of an intellectual elite and world bankers is surely preferable to the national auto-determination practiced in past centuries.
You can find a dozen sources or more for the second quote, none of them particularly reputable, by putting part of the quote in Google. Let's just assume for my argument that both quotes are fake; for my point it doesn't actually matter, because both serve to illustrate why people are so concerned with globalization.
The concern is, simply, that unchecked globalization will lead to the effective and collective loss of sovereignty of the nations, to be replaced by a supranational, unelected, and unaccountable Power that will be almost impossible to displace.
Rockefeller himself denied having an "elected" world government as a goal, but the question was, why is globalization disdained. The "Illuminati" type conspiracy theories out there, even assuming they are pure fantasy, show you why. As does the fictional "1984". As does the example of ancient Rome. It is a fear that, if a Power arises that effectively rules the entire world, there may be no going back, and there may be no way to stop the emergence and total corruption of a global state.
An early draft of the Declaration of Independence says:
But when a long train of abuses & usurpations, begun at a distinguished period, & pursuing invariably the same object, evinces a design to subject them to arbitrary power, it is their [mankind's] right, it is their duty, to throw off such government & to provide new guards for their future security.
If unchecked globalization is a road that leads eventually to unprecedented tyranny, the same philosophy that gave rise to the Declaration would therefore stand opposed to it.