Technically speaking, this is true. However, it is also a strawman. In practical terms, the constitution can be changed by reinterpreting it, which is within the purview of the Supreme Court.
The constitution states the amendment process:
The Congress, whenever two thirds of both Houses shall deem it necessary, shall propose Amendments to this Constitution, or, on the Application of the Legislatures of two thirds of the several States, shall call a Convention for proposing Amendments, which, in either Case, shall be valid to all Intents and Purposes, as Part of this Constitution, when ratified by the Legislatures of three fourths of the several States, or by Conventions in three fourths thereof, as the one or the other Mode of Ratification may be proposed by the Congress; Provided that no Amendment which may be made prior to the Year One thousand eight hundred and eight shall in any Manner affect the first and fourth Clauses in the Ninth Section of the first Article; and that no State, without its Consent, shall be deprived of its equal Suffrage in the Senate.
However, this ignores the fact that the Supreme Court can “reinterpret” the constitution.
For example, the federal government is barred from taking powers not explicitly granted by the constitution by the tenth amendment:
The powers not delegated to the United States by the Constitution, nor prohibited by it to the States, are reserved to the States respectively, or to the people.
Between 1917 and 1919, this was interpreted to mean that the government may not outlaw foods or drinks, especially if they are manufactured and consumed in the same state. Therefore, to pass prohibition it was necessary to pass the 18th amendment:
Passed by Congress December 18, 1917. Ratified January 16, 1919. Repealed by amendment 21.
After one year from the ratification of this article the manufacture, sale, or transportation of intoxicating liquors within, the importation thereof into, or the exportation thereof from the United States and all territory subject to the jurisdiction thereof for beverage purposes is hereby prohibited.
The Congress and the several States shall have concurrent power to enforce this article by appropriate legislation.
This article shall be inoperative unless it shall have been ratified as an amendment to the Constitution by the legislatures of the several States, as provided in the Constitution, within seven years from the date of the submission hereof to the States by the Congress.
Yet today, without any relevant change in the constitution itself, the federal government runs the Drug Enforcement Agency that forbids other drugs.
Very few people are afraid that the government will abolish the second amendment from the written constitution. But if it is interpreted to mean “the state militia may bear arms”, or “only such arms as existed when the Bill or Rights was ratified”, it becomes dead letter.
This fear is based on: