The point is that CONTINUE and BREAK jump to exactly one location given their lexical context and cannot jump anywhere else. They are also only meaningful when applied to structured control flow. The problem with GOTO is the unbound nature of its jump target, which leads to control flow that is difficult to comprehend by looking at the lexical structure of a function.
It's a subtyping problem, and you have the is-a relationship backwards: a cat is an animal but not every animal is a cat. GOTO is a BREAK (could always be substituted for one), but a BREAK is not a GOTO.
When you need a BREAK you could implement that in terms of GOTO, but no amount of coercion will allow you to use a BREAK as a generic GOTO.
You wrote this backwards, but you seem to understand the relationship and that GOTO is more general. That is, every BREAK is a GOTO (because you can always substitute a GOTO), but every GOTO is not a BREAK (i.e., you can't substitute a BREAK for some GOTOs because BREAK cannot jump to an arbitrary label).
A GOTO is just one possible implementation of BREAK, just as a cat is one possible implementation of an animal.
The practical impact of this is that it is incorrect to ascribe to BREAK the same weaknesses as GOTO, because BREAK is not a GOTO.
I agree that CONTINUE and BREAK are easier to reason about because you can look at them and instantly know what they do without having to look up what label they're jumping to.