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Adding together the numerical values that denote the length of his lifespan in years and minus one times mine, we would get a number bigger than zero.
You indicate that "He is older than I" requires another word, such as "thought." If that were the case, then it would equally be true of "He is older than me."
Of course, that would sound very incorrect. The reality is that "He is older than me" is actually incorrect for that very reason. The sentence requires a subject ("I") and not an object ("me.)
Now, you will hear people use "me" but most people will know it is a colloquialism and not, in fact, grammatically correct.
To many people, both versions sound incorrect. Hence, we would say "He is older than I am."
"He is older than me" is grammatically incorrect? Then most of us are wrong.
He is correct to state that after 'I' there has to be something. He might not know, however, that something is there, actually, that something is understood but has been removed via resort to ellipsis of the whole predicate. The preposition 'than' followed by a pronoun in objective case, on the other hand, makes the sentence complete, he might think with partial, if not full, justification, especially if we take into account that the only minute detail that Nightmare, our indomitable warrior, is missing is the fact that by origin, 'than' is a subordinating conjunction and not a preposition. Even though it is ill-founded, I have to hand it to Nightmare that his logic has its moments.
Same case must be compared in a sentence.
He is older than I.
"He and "I both are Nominative
He is older than me
"He" is nominative while "I " is Accusative.
It actually does become clearer when we consider that the sentence is actually short for "He is older than I am." We can very naturally and correctly drop off the "am." But what if we try to then complete the sentence: "He is older than me"? What word would you use: "am" or "is"? Clearly we can't use either one. The original sentence is simply incorrect.
I'd appreciate your further thoughts on this. You may well have a better command of the language than me.
But your point about what should be taught as being correct on this forum is a good one. Consistency is also always a good thing.
But where is the virtue in teaching that "He is older than me" is wrong when everybody says it? It's similar to the singular "they". If learners are going to actually speak English (rather than just doing grammar exams) they want to know how they should say something.
Since "He is older than me" is accepted by educated people in all major English speaking countries (on present evidence), then this should be considered an exception to the rule, rather than being called "incorrect".
Grammar describes how a language works. Although grammar has a useful prescriptive function, and one that teachers and students should respect, the majority usage of a term such as this makes it idiomatic, and hence not "incorrect".
At least that's my viewpoint.