I may be wrong but my understanding of evolution does not contradict the statement: "All human beings are descendants of Adam."
On the contrary, it certainly does contradict such a statement.
The Mitochondrial Eve concept refers to the single human woman through which all living humans today descend through their mother. Conversely there is a Y-chromosomal Adam which is tracing all living humans to a single male heir through their father.
The complication is that those two, ME and MA, lived thousands of years apart from each other. In fact MA lived roughly 110,000 years later than ME. What this means is that humans prior to the birth of MA must have been born of a descendant of ME and some other male which may or may not have been an ancestor of the eventual MA. Its guaranteed that "All human beings are descendants of MA," is false.
Now you might be arguing that we should simply define ME's partner as being "Adam", but that leaves the 110,000 year gap with all those human males that are not descended from "Adam" until MA is finally established.
Or you might argue that once MA is established beside a long descendant of ME that couple should be defined as "Adam" and "Eve". But that still doesn't work because for your statement to be true all previous generations leading up to that must be redefined as being something other than human, a distinction serving no purpose other than to validate your statement.
So no, your statement "All human beings are descendants of Adam," is completely contradicted by evolution and our biological knowledge.
You could be right if you said "all of the current human population", going back a few thousand years you reach a point where a high proportion of the entire human population are all common ancestors of the current population.
But you still don't get ancestry from a single male-female pairing, and the population models are bunk. Its irrelevant what could possibly happen if humans did nothing but have sex, make babies, never died of anything but old age, and had no resource limitations.
Especially when our biological and archaeological facts support humans coming out of Africa up to 200,000 years ago.
I am referring to the YEC models that try to claim humans have only been breeding for roughly 6000 years. The OP's claim about being descended from Adam implies the belief that the event described in the Bible occurred.
While it is certainly possible that the human line could be traced wholesale back to around 500AD, the idea that the entirety of humanity is descended from two individuals from such recent a pairing is patently ridiculous.
Wounded King writes:
There might well have been someone around at that time, amidst the thousands of contemporaneous common ancestors,
Solely, you need to put 'solely' or 'just' in their somewhere because the entirety of humanity is descended from two individuals from such a recent pairing as well as from another few million other such pairings around the same time.
OK true, but you wouldn't parse the statement "Humanity is descended from Adam" to mean that there is at least one living human alive today that descended from someone named Adam, and the rest of humanity is composed of offspring from other family lines.
If we are to use such a tortured interpretation then we can conclude that the original statement was technically true but mostly meaningless. (and by most accounts deceptive)
What I said was 'because we have someone like ME, my statement is not false.'
No, thats still false. Since that statement only technically talks about ME, and your statement only addresses Adam, they don't mesh at all. ME existed long before YcA ever cropped up, so her descendants would have had many different male lines to mate with.
What you could say is: "Because there is someone like YcA mating with an established ME, my statement was not false assuming terms used within it are redefined to match the biological theory." "Adam" would need to be a placeholder for the unknown YcA, and "humanity" would need to be redefined as only meaning "living humans".
Not that I even understood what you mean by this comment. But ... Does this also mean that because "humanity" is not only "living humans", ME is false?
No, ME is a specific individual among the human species from which all living humans descended. Before and even during her time there were humans which were not descended from her line. The ME idea specifically describes this relationship.
The original statement was "All human beings are descendants of Adam." That would seem to mean that if you examined any human they would be a descendant of Adam (or Adam himself). This is in keeping with the set of beliefs that would lead to such a statement in the first place.
I might otherwise be willing to excuse an imprecise colloquial usage of language except that the OP is clearly trying to squeak through on technicalities and redefinitions. If he wants to be technically not disproved then he is going to have to live with being technical with our terms.