There are two types of fermions - Dirac's and Majorana's. Majorana's fermions are their own antiparticles and they have not been detected yet. Sometimes, it is conjectured that e.g. neutrinos could be Majorana fermions.
However, it seems to me that there should be no Majorana fermion in current Universe. When particle and its antiparticle meet, they anihilate each other. Since there is no distinction between particles and antiparticle in case of Majorana fermions, a bunch of Majorana fermions should completely anihilate (maybe one particle can surive in case there were odd number of the particles in the bunch). This should happen shortly after Big Bang when all type of particle were created and the Universe was still small. Perhaps we could create Majorana fermions in accelerators, however, I suppose we should not be able to detect them in the Nature.
Does my reasoning make sense? If not, what am I missing?