Andrews was born in Templeton, Massachusetts, on March 22, 1812, "the youngest of eight children of the Reverend Elisha Andrews and his wife, Ann Lathrop." He grew up thirty - five miles northeast in Hinsdale, New Hampshire. Andrews went to Louisiana at age 19 and studied and practiced law there. Appalled by slavery, he became an abolitionist. He was the first counsel of Mrs. Myra Clark Gaines in her celebrated suits. Having moved to Texas in 1839, Andrews and his family were almost killed because of his abolitionist lectures and had to flee in 1843. Andrews travelled to England where he was unsuccessful at raising funds for the abolitionist movement back in America.

While in England, Andrews became interested in Pitman's new shorthand writing system and upon his return to the U.S. he taught and wrote about the shorthand writing system, and devised a popular system of phonographic reporting. To further this he published a series of instruction books and edited two journals, the Anglo - Saxon and the Propagandist. He devised a "scientific" language, "Alwato," in which he was wont to converse and correspond with pupils. At the time of his death Andrews was compiling a dictionary of Alwato, which was published posthumously. A remarkable linguist, he also became interested in phonetics and the study of foreign languages, eventually teaching himself "no fewer than 32" languages.

By the end of the 1840s he began to focus his energies on utopian communities. Fellow individualist anarchist Josiah Warren was responsible for Andrew's conversion to radical individualism, and in 1851 they established Modern Times in Brentwood, NY. He was elected an Associate Fellow of the American Academy of Arts and Sciences in 1846. In 1857 Andrews established Unity Home in New York City. By the 1860s he was propounding an ideal society called Pantarchy, and from this he moved on to a philosophy he called "universology", which stressed the unity of all knowledge and activities. He was also "among the first Americans to discover Marx and the first to publish his Communist Manifesto in the U.S."

Andrews was one of the first to use the word "scientology". The word is defined as a neologism in his 1871 book The Primary Synopsis of Universology and Alwato: The New Scientific Universal Language. In the 1870s Andrews promoted Joseph Rodes Buchanan's Psychometry besides his own Universology predicting that a priori derived knowledge would supersede empirical science as exact science. Andrews was also considered a leader in the religious movement of Spiritualism.

Like most of the nineteenth century individualist anarchists, and unlike the anarcho - communists, he supported the right of employment and wage labor. However, he believed that in the system within which he was living that individuals were not receiving a wage commensurate with the amount of labor they exerted. He said:

The 'Wages System' is essentially proper and right. It is a right to that one man employ another, it is right that he pay him wages, and it is right that he direct him absolutely, arbitrarily, if you will, in the performance of his labor, while, on the other hand, it is the business of him who is employed implicitly to obey, that is, to surrender any will of his own in relation to a design not his own, and to conceive and execute the will of the other... It is right that the great manufacturer should plan, and either alone, or through the aid of assistants under his direction, organize his mammoth establishment. It is right that he should employ and direct his hundreds, or his five hundred men... It is not in any, nor in all of these features combined, that the wrong of our present system is to be sought and found. It is in the simply failure to do Equity. It is not that men are employed and paid, but that they are not paid justly…

For Andrews, to be paid "justly" was to be paid according to the "Cost Principle," which held that individuals should be paid according to the amount of labor they exert rather than according to the benefit that another receives from that labor (the latter being called the "Value Principle"). To help make this simple, he, after Josiah Warren, advocated an economy that uses "labor notes". Labor notes are a form of currency marked in labor hours (adjusted for different types of labor based on their difficulty or repugnance). In this way, it is not how much the employer values the employee's labor that determines the employee's pay, but simply how much the employee has labored. For similar reasons he did not believe people should be paid interest for loaning capital; in other words, he did not see the loaning of capital as requiring any labor or deprivation on the part of the loaner. He insisted that the benefit received from goods or labor is not a just measure of price.

Every variety of interpretation has been put upon my opinions, usually the least favorable which the imagination of the writer could devise, with a view, apparently, of cultivating still further the natural prejudice existing in the public mind against any one bold enough to agitate the delicate and difficult question of the true relations of the sexes, and the legitimate role which the Passions were intended to play in the economy of the Universe. In the absence of any readiness on the part of the public to know the truth on the subject, false, extravagant and ridiculous notions have flooded the country in its stead. I reject and repudiate the interference of the State, precisely as I do the interference of the Church. A grand social revolutions will occur. Tyranny of all kinds will disappear, freedom of all kinds will be revered, and none will be ashamed to confess that they believe in the Freedom of Love.