Take the idea of a dependent origination process, a kind of causal thread running between lives. I suppose the argument is not that such a thread doesn’t exist at all, but that this process isn’t worthy of the label “atta” (or “soul”) though some people might be inclined to attach that label to it.
Karunadasa does also argue that the idea of atta being something one should have full control does crop up in the sequence of the three characteristics, i.e. why does something being a source of dukkha necessarily imply it is anatta? :
In fact, it is this same idea of atta that comes into focus in the logical sequence or interconnection between the three signs of existence (tilakkhana), namely impermanence (anicca), suffering (dukkha) and anatta. How the first two characteristics lead to the idea of anatta is shown as follows:
"Whatever is impermanent is suffering (yad aniccam tam dukkham); whatever is suffering is anatta (yam dukkham tad anatta)"
The question that arises here is why the idea of anatta is said to follow as a corollary from the fact of dukkha or suffering. This should become clear if we examine the three signs of existence in their reverse order. When examined in this context, the following facts become clear: I cannot consider anything as my own or as belonging to me (=atta), because whatever I consider so, is a source of suffering (dukkha). Why is it so? Because what I mistakenly consider as my own does not behave in the way I want it to behave. Why is it so? Because whatever I mistakenly consider to be my own is subject to constant change (anicca).
Or going back to this thread/DO process:
What is denied in Buddhism is not the concept of person which is called puggala, but a self-subsisting entity within the puggala, which answers to the definition of atta. Therefore, Buddhism has no objection to the concept of puggala, if by puggala is understood, not an entity distinct from the sum total of the properly organized five aggregates, nor a substance enduring in time, nor an agent within the five aggregates. The puggala (person) is the sum total of the five aggregates combined according to the principles of dependent origination and which are constantly in a state of flux.
I suppose to clarify what is being negated/denied in the term anatta, it’s necessary know what exactly is positively meant by “atta” (perhaps not such a straightforward thing to do! ).