An awesome historical investigation of why terminals were 80×25:"Because the paper beds of banknote presses in 1860 were 14.5 inches by 16.5 inches, a movie industry cartel set a standard for theater projectors based on silent film, and two kilobytes is two kilobytes" is as far back as I have been able to push this, but let's get started.
In August of 1861, by order of the U.S. Congress and in order to fund the Union's ongoing war efforts against the treasonous secessionists of the South, the American Banknote Company started printing what were then called "Demand Notes", but soon widely known as "greenbacks".
It's difficult to research anything about the early days of American currency on Wikipedia these days; that space has been thoroughly colonized by the goldbug/sovcit cranks. You wouldn't notice it from a casual examination, which is of course the plan; that festering rathole is tucked away down in the references, where articles will fold a seemingly innocuous line somewhere into the middle, tagged with an exceptionally dodgy reference. You'll learn that "the shift from demand notes to treasury notes meant they could no longer be redeemed for gold coins[1]" -- which is strictly true! -- but if you chase down that footnote you wind up somewhere with a name like "Lincoln's Treason -- Fiat Currency, Maritime Law And The U.S. Treasury's Conspiracy To Enslave America", which I promise I am only barely exaggerating about.
Previously, previously, previously, previously, previously, previously, previously, previously.
I had forgotten that the VT100 had a 25th line. Let's see, can I find a copy of the sysline man page and does it have a list of 25-line terminals...? Yes and yes. "Not all terminals contain a status line. Those that do include the h19, concept 108, Ann Arbor Ambassador, vt100, Televideo 925/950 and Freedom 100."
I don't think that's right. 80x24 was long the standard for ASCII terminals. I worked on VT52s, VT100s, and H19s while at Heathkit in the late 1970s. They all had 24 lines, not 25, and there was no status line. The VT100 had a neat trick where it would display 132 columns instead of 80 if fitted with more memory, but still 24 lines.
The IBM 3270 had 25 lines so that it could show 24 lines of content with one line for a typed command, which was necessary because it couldn't send an interrupt on any keystroke except ENTER and so could not support an emacs-style editor. I messed with several in college. The original PC had an 80x25 text mode to support 3270 emulation.
I think the author of the article was misled by bad information. In particular, this StackExchange thread has a lot of untrue content.
Sovcits are adorable.