From your link:
Dirac came out of his depression when he received a phone call from his friend Abdus Salam, saying: "Relax Paul, my friend Nino Zichichi has discovered the antideuteron".
This is the opposite of the summary in your question (v1) which suggests that Dirac believed for some reason that the antideuteron shouldn't occur and was upset when it was found.
The position of the article is as follows. The prediction of the anti-electron is, as Dirac discovered, a mathematical result of trying to satisfy the symmetries of the Lorentz transformation when describing the interaction between electromagnetic fields and charged objects with spin-half. The simplest acceptable spinor winds up having four components with the same mass: two with one sort of charge which transform into each other under rotations, and two with the other sort of charge which transform into each other under rotations. This is more or less the same QED that we use today and is quite general, describing the interaction between the electromagnetic field and the electron; the electromagnetic field and the proton, thus predicting antiprotons; and the electromagnetic field and the neutron, predicting antineutrons. (Remember that the neutron couples to electromagnetism because it has a nonzero magnetic moment.)
However, Dirac's quantum electrodynamics makes no effort to describe strong or weak nuclear forces.
In 1965 there wasn't yet a good theoretical treatment of the strong nuclear interaction.
There was experimental evidence for the anti-electron, the anti-proton, and the anti-neutron, with the same masses as their matter counterparts; however it was experimentally possible that the anti-proton and anti-neutron would interact via some antimatter-specific strong interaction that was not the same as the matter version.
A probable consequence of a distinct anti-strong force would be that the anti-deuteron, an anti-proton and anti-neutron bound together by the anti-strong force, would probably have a different binding energy, excitation spectrum, and mass than the matter deuteron, if it were stable at all.
If the deuteron, $d$, and its antiparticle, $\bar d$, had different masses,
even though $m_p=m_\bar p$ and $m_n = m_\bar n$,
an experimenter could distinguish between a matter universe and an antimatter universe by capturing neutral baryons on charged baryons and measuring the wavelength of the photons that are emitted. (It's a 2.2 MeV photon, whose energy/wavelength is known at the part-per-million level based on its diffraction through a perfect silicon crystal, which is a great paper you should read sometime.)
But that breaks CPT symmetry: reverse time, invert space, flip all the charges, and everyone should agree on lengths and on scalars like masses.
The combined symmetry CPT is a consequence of invariance of spacetime under Lorentz transformations --- but it was invariance under Lorentz transformations that we used to predict antimatter in the first place.
You can see why Dirac would have been agitated by the possibility.
Lorentz invariance, and therefore invariance under the combined transformation CPT, is a starting assumption for all modern quantum field theories, including quantum electrodynamics, quantum chromodynamics, and the theory of the electroweak interaction. When your article's author writes that "at the Planck energy ... CPT invariance breaks down," I'm not entirely sure what he has in mind. (I have some ideas, but this already-long answer isn't the place for me to work through them.) There isn't any contemporary theory that includes CPT-breaking, just like there isn't any contemporary theory that makes solid predictions of what happens and Planck-scale energies.
There are some folks who are thinking about CPT-breaking phenomenology: if Lorentz invariance is only an approximate symmetry and you looked at this observable in that system, you might see such-and-so effect. But an observation like that would be a puzzle to be explained, not the fulfillment of any prediction.