Our system has underpinning it unalienable rights that are enshrined in our Constitution that no law approved by the majority are allowed to remove (Article VI, Section 2 US Constitution). And all States are bound to uphold this aspect of the Constitution in the due course of the Law (14th amendment, Section 1).

So there can be things that the majority support but can never be enforced because the Constitution overrides that as a right granted to all people and is irrevocable in nature without obtaining the bar set forth in amending the US Constitution. That's why fundamental rights are incredibly important, because there does exist times when the majority subjugates some minority and that goes contrary to pretty much the charter of the United States.

We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness.--That to secure these rights, Governments are instituted among Men, deriving their just powers from the consent of the governed

(US Declaration of Independence)

In this they are indicating that by the nature of existence (and in this case they indicate that is endowed to them via a Creator) that there exists things that no Government, no entity, not anything can remove from the people and then give three examples of those things. The second part indicates that it is the charter of Government to secure those rights, to fight things that may seek out to remove them from the people. And that the power that Government gets to do that thing is derived from the people. Because remember, up to this point (minus the French Revolution), Governments had power because "God" said so. In this case, a person has power not because of "God" but because of people. This is a big difference in how Governments get ran now. The one in charge is held to account not by "God" but by the people.

Prudence, indeed, will dictate that Governments long established should not be changed for light and transient causes; and accordingly all experience hath shewn, that mankind are more disposed to suffer, while evils are sufferable, than to right themselves by abolishing the forms to which they are accustomed.

(US Declaration of Independence)

And this is one of those things that's really shows how well the people who wrote these documents understood mankind. Basically this statement is saying "people don't just overthrow their governments on a whim". But deeper it is saying, people are such that they adjust to suffering and being denied basic human rights because they are comfortable with the suffering they receive. And while this is a good point to overthrow the government, it's also an important highlight that any government wishing to endure, enshrine rights that preempt that suffering.

And there's so much more the people who created this nation had to say about all of this, but it boils down to, there has to be some line in the sand that no matter if 100% of the people support it, we just cannot cross it without a monumental effort to do so. That sometimes, the majority is very wrong and they need something to stop them and have them seriously think about the consequences of what they are asking.

People who say this kind of nonsense about "the majority support them" are the same folks who have zero clues about civics and the nation that they live in.