Is the classification of particles into matter and anti-matter arbitrary? It is well known that every fundamental particle has a corresponding antiparticle, and that  – except for particles which are their own antiparticle – for practically every pair of particles and antiparticles, one type of particle predominates. We call this particle matter, and its antiparticle is considered to be antimatter.
However, is there any intrinsic difference between matter and antimatter, or are these terms defined based on nothing more than the balance that we so happened to end up with? For example, is there any reason that we should place an up quark and a charm quark in the same category, and not an up quark and a charm antiquark? Is there any reason we should group together up quarks and electrons rather than up quarks and positrons?
 A: You are confusing two things at least.
This is the particle table:

There exists a mirror antiparticle table such that when the quantum numbers of particle and antiparticle are added each sum is identically zero, and particle and antiparticle have the same mass.
When a particle meets an antiparticle , and both are at rest, they annihilate  into energy, that comes out with new particle pairs with different particle quantum numbers.  For example : an e+  scattering on an e- with enough center of mass  energy can give a proton antiproton pair.
The table is such that the standard model of particle physics makes sense, and then  one has protons, neutrons made up of quarks so that the charges make sense with the data. Baryon number is carried by quarks and is +/1/3 so you cannot add an antiquark and expect to get a baryon, etc.etc.
The standard model encapsulates the data and is very successful most of the ime in fitting new experimental data.
A: The definitions have a pure historic reasoning which has to do with the order of verification of the existence of particles. The names stuck in the scientific community because a radical redefinition of names to suit language would be impractical and confusing. 
As for the grouping of particles, it has strong mathematical grounding. The particles are grouped according to the similarities they possess between each other, and the mathematics are described by Group Theory.
