Antimatter shares many properties with ordinary matter. Antiparticles have the same masses as their matter counterparts, but, Antimatter is made of particles that have an opposite sign to those of matter, so a proton is positively charged, whereas, its antimatter equivalent is called antiproton, which has a negative charge, they both fall in a gravitational field. So yes, antimatter is a sort of matter. It is still confusing to scientists why there is so much matter and so little antimatter in the universe, since they must be made in equal quantities in high-energy interactions. Like the Big Bang (Pairs of matter and antimatter particles can be generated from big concentrations of energy. This is what happened during the Big Bang, an explosion so intense that generated matter and antimatter where there only were immense quantities of energy.)
As for the name, it is arbitrary. If we were all made of antimatter, then we probably would still call or consider it the equivalent of “matter”, and call/consider the other stuff we aren’t made of “antimatter”. The universe would still work just fine if all the matter were swapped for antimatter, we would still be the same. The whole thing balances.. It’s just a matter of what we call matter or antimatter. (Heehee..okay no, that was exceedingly lame) Suppose we detect signals from a faraway, alien civilization. They inform us they are going to visit our planet. We would like to check first if they are made of matter or antimatter, as the latter situation would prove disastrous if they try to shake our hands—BOOM! ( This is like what happened in the big bang, however, I would also like to add that the opposite process of what occured in the big bang theory is also possible When a particle of matter meets its corresponding antimatter particle, they both disappear. The process is called annihilation and entails a transformation of all the mass into energy (in the form of photons, in particular gamma rays highly energetic and penetrating)). They insist that they are made of matter, but that isn’t convincing enough—how do we know that what they call matter isn’t what we call antimatter?
Basically, we’d be the same, because we’d be accustomed to living like we are now.