I'm taking organic chemistry right now, and we have just been introduced to the concept of anti-bonding orbitals. I get that the point of the anti-bonding orbital is to conserve orbitals during bonding, but since orbital theory is just a mathematical concept which maps the probability of where an electron has the highest chance of existing, the orbitals themselves carry no physical meaning. Why must the model account for conservation of orbitals when it seems equally convenient to just leave them out?

Please explain like I have taken some calc II and linear algebra.