Is nothing impossible, as cladistics and particle physics claim?

It is often said that nothing is impossible. But, is it true? Is actually nothing impossible?

Assuming that it is true means that everything is possible. Now, if everything is possible, then it is possible to both eat the cake and keep it at the same time, which obviously is impossible. There thus is at least one thing that isn’t possible (ie, is impossible): to both eat the cake and keep it at the same time.

The statement that nothing is impossible is thus false. It is actually impossible to both do and not do at the same time. This limitation is actually what stands between us and the truth (like “the true tree of life” of cladistics and “Higgs particle” of particle physics). They would have been true if this limitation would not have existed, which it, unfortunately, does.

The most surprising component in this matter is, however, that particle physicists claim that they have found empirical evidence (ie, Higgs particle) of that we indeed can both do and not do at the same time, If they are right, then it is thus possible to both eat the cake and keep it at the same time. This would indeed have been an empirical discovery worthy of the Nobel Prize if they indeed could have demonstrated it empirically, ie, eating the cake and keeping it at the same time, which they, of course, can’t.

The answer is thus no, everything isn’t possible. It is not possible to both do and not do at the same time, ie, to  both eat the cake and keep it at the same time. Particle physics’ empirical discovery that it is possible must thus be a devastating mistake. How particle physicists could even think that it is possible is surprising, to say the least. Exactly what lead them out on this return alley?