The word “alot” meaning the opposite of “alittle” never existed in formal writing. What you were taught I can’t speak for. Even “a lot” is considered fairly informal.
(The word “alittle” never existed either.) “Allot” is a word.
Relatedly, what is the status of “cannot” these days? I was always taught that using “cannot” was a horrible sin, but lately a lot of spell checkers helpfully extract the spaces from my "can not"s for me.
“Cannot” has been correct English all my life (and I am fairly old now). Indeed, I would say that it has a slightly different meaning from “can not”:
I cannot dance = I am unable to dance.
I can not dance = I am not compelled to dance.
In most contexts, “cannot” is the form you want (or “can’t”, which is a contraction of “cannot”, not of “can not”).
I think you were taught wrong; your spellchecker is correct.
I see that Wiktionary (bless its little descriptivist heart) actually lists alot as a "nonstandard spelling of “a lot” (and it is also a town in India), but, as other posters are saying, it has never been “good” standard English (and even the OED which includes a lot of weird, non-standard stuff - even Canadian stuff - does not list it).
It’s because “a dozen”, etc. is still perceived by most English speakers as specifying a particular amount or number, whereas no one thinks of a “lot”* anymore when they hear “a lot” – it’s just perceived as a phrase which, taken as a whole, signifies “much” or “many”.
A bit like we never stop to question what exactly we are standing under when we “understand” something.
Or, to use an example from another language, whenever a French speaker says something negative (e.g., “I don’t know” = “je ne sais pas”), they don’t think to themselves “I don’t know EVEN A SINGLE STEP” – the original meaning of the “pas” part. Now, they just parse “pas” as meaning “not”.
(*These days, “lot” by itself usually means nothing more than a parking lot. Judging from the phrase “a lot”, it used to be used for more things than that – a portion, as in “allotment” or “lottery” – but there’s no special reason why it happened to become such a generalized phrase. It could have just as easily happened to, say, “a heap” (closer to the Spanish equivalent, “un monton”) – but it didn’t.)
It may be an age thing also, I am in my mid forties and as I said I distinctly remember learning that in grade school, which would have been in the 1970’s. I had noticed it in spell check occasionally but it was recently pointed out to me when I was doing some editing for a friends music and he said I made a mistake. I have no problem admitting to a mistake but I know that this was what I was taught in school, otherwise I would not have used it for 30 years.
Just a WAG, but perhaps, back in grade school, you and/or your teacher confused the “a lot/alot” issue (only the former is accepted in Standard English) with the “all right/alright” issue – “alright” is very informal, but is not, AFAIK, as universally unacceptable in Standard English as “alot” is.
A “lot” was in a near-obsolete usage an arbitrary grouping of items (which might be a single item), for purposes of dealing with discrete lots, each “lot” together but separately from other “lots.” In auctions, for example, a set of matching end tables and coffee table might be sold together as a single lot, while a group of a dozen Elvis-on-velvet prints might be another lot. In trading stocks, 100 shares is a ‘round lot’ while a quantity of less than 100 shares is an ‘odd lot’.
There’s a very short intellectual jump from “I bought a lot of furniture at the auction today” to “I bought a lot of groceries at the store” when both can mean a large arbitrary grouping.