If you see irony here, then as experienced an edition warrior as you are, you have somehow failed to apprehend the fundamental nature of the disagreement you are currently allowing yourself to be trolled over.
I'm proceeding in this discussion in as calm and considerate a manner as possible. That includes not assuming that Oofta is trolling, and not leaping to conclusions about the fundamental whatever underlying a statement.
So I'm engaging only with the statements, themselves.
5E eldritch knights can cast spells, which are described in the fluff as spells and justified by the character studying magic. 4E fighters could create effects which to many people seem obviously magical, but which the fluff "explicitly" denies to be.
The irony is in blithely accepting the arbitrary definition of what is and is not magic in one case, but bitterly denying it in the other, even though any definition of magic (a thing that, afterall, does not exist), is going to be arbitrary.
No 4e fighter power shot flames at his enemies or conjured monsters or did anything /obviously magical/, by any reasonable definition. They did things that were improbable, superhuman, or over-the-top-action-tropes, sure - more or less so depending on how you described them.
But not supernatural, and explicitly not magic, and mechanically as well as conceptually, quite distinct from casting spells.
You seem to be under the impression that citing that denial is a silver-bullet solution to the problem, but really it's just restating the problem. To your opponents, it looks like a contradiction of the objective facts about what the character is doing. Ridiculous, dissonant, possibly even disingenuous.
There are no objective facts about what the character is doing, the character exist only in imagination. The objective facts are there between the covers of the books (and in increasingly difficult to find errata). How you imagine what your character is doing when he uses his power was explicitly up to you as the player. So if you pictured something you found dissonant or ridiculous, the fault lay with your imagination or your judgement. If you found something someone else described dissonant or ridiculous, while they found it awesome, well,
that's a difference of opinion...
If there'd been a line in the PHB to the effect that everything the wizard does is just card tricks, would you (a) accept and repeat the line as incontrovertible proof that the wizard isn't magical, or (b) think the line is stupid?
There is no such line, and it would in no way be comparable to what was in 4e.
However, a lot of D&D does stray into science-fantasy, based as some of it is on works like the Dying Earth. It would not be too crazy for a D&D campaign to eventually reveal that the 'magic' everyone's been using - even the finger-wiggling, gibberish-mumbling 'spellcasting' - was all just "sufficiently advanced technology," a reality-altering Krell Thought Machine at the world's core, like in Forbidden Planet, run by a rather eccentric AI, for instance.
Because that's how the people you're addressing feel about the fighter. I'm not asking you to agree with them. But I am asking you to understand them
I can't go jumping to conclusions about what they feel or why.
"it's not magic because the book says it's not" is unlikely to be a productive avenue of argument.
There's a lot more to it than just that. Exploits and spells have more keywords exclusive to eachother than just Martial and Arcane, and do quite different things. Typed damage, for instance. Most spells that do damage, do typed damage, virtually no martial attacks do. There is just no factual basis in the actual game itself for the assertion "fighters cast spells."
To get to any 'underlying disagreement,' we must first dispense with the factual misstatements. If that underlying disagreement cannot be expressed honestly, then, honestly, it has no standing, and must be dismissed out of hand.
I and my group were of the opinion that many martial powers were supernatural spell-like abilities
Again, that "opinion" is at odds with the facts - it's mushier and more ambiguous, but still clearly false.
that did not model actions a truly mundane fighter could achieve.
This, OTOH, is fair. (If I don't read it too literally... literally, of course any PC could model the actions a truly mundane character could achieve - eating lunch at the inn, walking down the street, chopping wood, etc, Rather, you point is that exploits /did/ model actions that a truly mundane person could not do, or at least, not attempt with even the slimmest hope of success or survival. For instance, the kinds of crazy things action heroes and figures in myth/legend/fantasy who would map to 'fighters' do all the time.)
A character or archetype in heroic fantasy that would be most closely modeled by a D&D fighter would certainly go around achieving things beyond what a truly mundane person could realistically do. They're extraordinary, even superhuman figures. A fighter limited in that way would not even 'belong' in the same game with other classes, not as a co-equal alternatives, anyway - an example of handling that kind of thing can be found in Ars Magicka.
