But まい and げつ are both onyomi readings… That’s what the both refers to.
Like I said, I get why you were confused. And I don’t disagree that it could be reworded, but it isn’t incorrect technically.
I guess it’s not that important at this point though.
Ah, ok, I see what you mean, yeah I didn’t even consider that’s what it meant
Then it should probably be “using the on’yomi readings of both” in that case
You should probably email them to recommend this change in phrasing. Also, you can edit your posts to add additional thoughts instead of replying to yourself. 
Yeah, but it helps to distinguish it for people already responding to a previous comment. Plus I sometimes overwrite what I wrote before by mistake
You are not alone!
Treat them as exceptions to what exactly? Also left it out from your chart is that every other day counting from 11 and up except 20 and the days that end in four (like 14 and 24 which can be よっか) use にち like:
三十一日
百日
千日.
Also, there are plenty of other words that use にち for the reading of 日 beyond your list for example 日時.
I’ve come to think of 何月 as the special ?th month, called “What?-uary”. It’s like,
A: In What?-uary is the party?
B: It’s in February.
That’s how I group it with the month names in my head. Maybe it’s stupid, but it works.
You use がつ when 月 is immediately preceded by a number, or a placeholder for a number (何 is taking the place of a number); in all other case of the 音読み (on’yomi), you use げつ.
Just clarify more on this, がつ is used for the names of months or when asking what month. Counting the number of months uses ヶ月 read as かげつ. Just want to make sure that is more clear because based on how this is worded one could mistakenly assume that ２ヶ月 would use がつ.
日常 baby! Actually is there a 日 word that uses jitsu as the first kanji?
日月 (sun and moon, time, years) and 日外 (some time ago) apparently, but those are obscure as far as I can tell.
Awww, you left out the even longer 日月星辰. 
Well, that’s just 日月 and 星辰 glued together it seems Not uncommon for yojijukugo.
That is a fair point; I have changed my post to say “immediately preceded by a number” rather than just “preceded by a number”.
Even though the latter almost always implies the former, it is not incorrect to say in the following sentences, “bar” is preceded by “foo”. “in programming, foo is a placeholder name; bar and baz are others.”
The clarification further helps nonfluent English speakers, who may not get that nuance.
Well, considering how much confusion the OP already has, I just didn’t want that to be another source of confusion for them.
Exceptions to using じつ and げつ everywhere. That’s my chart of words that appeared until lvl 5 which is as far as I got so far, I’m sure there are more words with 日 and 月 yet to come.
Using にち is not an exception to any actual rule. Especially as にち is used more often as the reading for 日 in jukugo than じつ.
I think part of the problem in this thread you have is that you keep trying to invent rules that aren’t and thus causing yourself unnecessary confusion. Like this newest one where you think にち is an exceptional reading for some reason.
Edit to add:
So I just want to point out that I’m not trying to criticize you. This has been mentioned in other threads by others, but often it is better to learn words as words, rather than trying to invent rules around how you mash various readings together because, outside very specific cases, many of these ad hoc rules seem to tend to trip people up as they go along in their learning because they will end up encountering numerous exceptions.
I just meant that among the words I know so far (there aforementioned incomplete table) there are only 2 instances of がつ so it’s easier to treat them as an exception and use げつ everywhere else, similarly with にち
I’m a programmer, I need patterns to remember sh*t 
This whole “rule” is just something I noticed while idling in a swimming pool, my brain just works that way, it looks for patterns in things I’m trying to learn to help me better organize them.
