The construction The reason is because X has been upsetting pedants for about four generations now. Don't worry about it: it is a fixed phrase and beyond grammatical niggling. Millions of people use it every day, in every register, and writers of the very first rank have used it for at least four hundred years.
If you want a reasoned discussion from a recognized expert you may consult the blog Motivated Grammar written by Gabe Doyle of the Language and Cognition Lab at Stanford University:
A mild amount of redundancy improves the likelihood of the message being transmitted correctly. The problem is when there’s too much redundancy, slowing down the rate of communication. (A common problem in children’s conversations, for instance, or a boring person’s stories.) Using because instead of that here doesn’t slow anything down, though — aside from the couple hundred milliseconds the additional syllable might cost the speaker — so I’m pretty unsympathetic to this complaint as well.
But I beg you, abandon the effort to understand the use of words by replacing them with their etymologies and dictionary definitions. That's not how any language works; it's a dead end for a learner.
There are several possible contractions, none of which are acceptable to all speakers. The only thing that is fully acceptable to everyone is am I not?.
The contraction amn't is used only in Scottish and Irish English. Most North Americans have never heard it, and unless I'm mistaken, most English people readily identify it as Scottish.
The contraction ain't I? used to be acceptable, but because of the condemnation of he ain't for "he hasn't/isn't" and other uses of ain't, the phrase ain't I? became tainted by association. Now you can't say "ain't I?" without sounding uneducated to many people. This probably sounded more acceptable three or four generations ago than it does now; language commentator William Safire still recommended its use in 1982.
In southern England people began saying something like an't I? in the late 17th century, pronounced ahnt. Because the southern English drop their rs, they later started spelling this as aren't I, with no difference in pronunciation. They preferred to use an unrelated word whose written form was familiar to them and whose pronunciation was the same.
When American r-keepers began noticing this in British writing at the beginning of the 20th century, it sounded crazy to them to have an r there. It made no sense at all, because there was no connection with the word are. So aren't I attracted considerable criticism. Nonetheless, it has gained acceptance over time, and now most Americans use it, since it's the only contracted form available to them that doesn't involve ain't.
Nowadays you'll find contradictory opinions on the acceptability of aren't I in writing, and particularly in formal writing. If you want to avoid controversy, stick to am I not? in writing. (The advice might differ if you're writing in Standard Scottish English, but I'm not qualified to comment on this.)
In speech and in writing meant to remain close to speech, there is a danger, alluded to in the comments, that am I not? will sound excessively stuffy and formal. In this case, aren't I? may be preferable, at least in England and North America.
Best Answer
To add to Stangdon's good answer, some grammarians use a more understandable term such as the plural-only nouns (Huddleston & Pullum, 2002).
There are several subcategories of plural-only nouns such as the bipartites (eg. "trousers", "pajamas", "bloomers"), words of compensation and reward (eg. "apologies", "compliments", "regards"1), and formal expressions of feelings (eg. "condolences", "thanks", "congratulations").
1 The singular counterparts of these exist but are generally used in different senses