The term “a dangerous age” is used most often to refer to the susceptibility to ideas, passions, and temptations of young people as they emerge from childhood and move toward adulthood.
Patricia Meyer Spacks, in a 1978 article titled “The Dangerous Age” (Eighteenth-Century Studies , Summer 1978, Vol. 11, No. 4) cites two 18th century providers of advice with colorful descriptions of the concept, though neither used the term:
I am so much aware of the Inconstancy and Unsteddiness of the human Heart, the Frailty of the best Resolutions, and the most obstinate Virtue we can boast, the fatal Power of Temptation, the terrible Effects of bad Company, and the almost irresistible Force of Example, and withal, the Difficulty of attaining that high Pitch of Virtue necessary to qualify for the Enjoyment of the Christian Salvation, that I tremble to think what Trials you, or any Youth under my Care, may have to go through, and of the dreadful Hazard you run in passing through Life. — James Burgh, Youth’s Friendly Monitor: Being a Set of Directions, Prudential, Moral, Religious, and Scientific (London, 1756), pp. 58-59
Alas, my brothers, in how many different directions may the young, the inexperienced, and the heedless, be trained on to destruction! In just as many as there are irregular inclinations to prompt, worthless companions to entice, and dangerous follies to ensnare them. — James Fordyce, Addresses to Young Men , 3rd ed., 2 vols. (London, 1789), I, 64
The earliest use of the term “dangerous age” in this sense that I could find in newspapers comes from earlier in the 18th century, in the Philadelphia paper American Weekly Mercury on October 16, 1735. It refers to youth
whose tender minds, like a fair Table, are capable of any Impressions, and are naturally disposed to receive such Doctrines as flatter their Passions, and open a larger Circle for the deluding Pleasures and Vanities to which that dangerous Age is most addicted — American Weekly Mercury, October 16, 1735, p1
An even earlier example appears in a play published in 1663. In the play — The Adventures of Five Hours: a Tragi-Comedy by Samuel Tuke — a character who had been charged with the care of an orphaned young woman “Rich, Beautiful; and Young”, tells the woman’s brother that his sister, though she was “much more expos’d to the great World than yours”
Yet, thanks to my Temper, cosin, as well as to her Vertue, I have seen her grow even from her Childhood, to her dangerous Age, without the least Disturbance to my rest.