This looks like a very fragile argument to me. Consider multiple conflicting goals. Consider vague general goals (e.g. "explore") with a mutating set of subgoals. Consider a non-teleological AI.
You assume that in the changeable self-modifying (and possibly other-modifying as well) AI there will be an island of absolute stability and constancy -- the immutable goals. I don't see why they are guaranteed to be immutable.
I cannot understand why any of these would cause an AI to change their goals.
My best guess at your argument is that you are referring to something different from the consensus use of the word 'goals' here. Most of the people debating you are using goals to refer to terminal values, not instrumental ones. ('Goal' is somewhat misleading here; 'value' might be more accurate.)
A stub on a point that's come up recently.
If I owned a paperclip factory, and casually told my foreman to improve efficiency while I'm away, and he planned a takeover of the country, aiming to devote its entire economy to paperclip manufacturing (apart from the armament factories he needed to invade neighbouring countries and steal their iron mines)... then I'd conclude that my foreman was an idiot (or being wilfully idiotic). He obviously had no idea what I meant. And if he misunderstood me so egregiously, he's certainly not a threat: he's unlikely to reason his way out of a paper bag, let alone to any position of power.
If I owned a paperclip factory, and casually programmed my superintelligent AI to improve efficiency while I'm away, and it planned a takeover of the country... then I can't conclude that the AI is an idiot. It is following its programming. Unlike a human that behaved the same way, it probably knows exactly what I meant to program in. It just doesn't care: it follows its programming, not its knowledge about what its programming is "meant" to be (unless we've successfully programmed in "do what I mean", which is basically the whole of the challenge). We can't therefore conclude that it's incompetent, unable to understand human reasoning, or likely to fail.
We can't reason by analogy with humans. When AIs behave like idiot savants with respect to their motivations, we can't deduce that they're idiots.