The crystal field splitting is based on where the ligands (modelled as point charges) are in relation to the orbitals. In an octahedral complex, the ligands are all at 90° from each other and are placed on each of the x,y,z axes. The orbitals that lie on these axes will experience the most repulsion and will rise in energy, while the orbitals between the axes ($\ce{t_{2g}}$) will lower in energy as they experience less repulsion from the ligands, and the average overall energy is maintained.

I can only assume that the degree by which the $\ce{e_g}$ orbitals are raised is the same due to the $\ce{d_{z^2}}$ orbital technically being a linear combination of what would have been the $\ce{d_{z^2-x^2}}$ and $\ce{d_{z^2-y^2}}$ orbitals. This means that the $\ce{e_g}$ orbitals lie on the axes to the same extent as each other, so experience the same overall repulsion from the ligands.

The crystal field splitting is based on where the ligands (modelled as point charges) are in relation to the orbitals. In an octahedral complex, the ligands are all at 90° from each other and are placed on each of the $x,$ $y,$ $z$ axes. The orbitals that lie on these axes will experience the most repulsion and will rise in energy, while the orbitals between the axes $(\mathrm{t_{2g}})$ will lower in energy as they experience less repulsion from the ligands, and the average overall energy is maintained.

I can only assume that the degree by which the $\mathrm{e_g}$ orbitals are raised is the same due to the $\mathrm d_{z^2}$ orbital technically being a linear combination of what would have been the $\mathrm d_{z^2-x^2}$ and $\mathrm d_{z^2-y^2}$ orbitals. This means that the $\mathrm{e_g}$ orbitals lie on the axes to the same extent as each other, so experience the same overall repulsion from the ligands.

The crystal field splitting is based on where the ligands (modelled as point charges) are in relation to the orbitals. In an octahedral complex, the ligands are all at 90 degrees from eachother and are placed on each of the x,y,z axes. The orbitals that lie on these axes will experience the most repulsion and will rise in energy, while the orbitals between the axes (t2g) will lower in energy as they experience less repulsion from the ligands, and the average overall energy is maintained.

I can only assume that the degree by which the eg orbitals are raised is the same due to the dz2 orbital technically being a linear combination of what would have been the dz2-x2 and dz2-y2 orbitals. This means that the eg orbitals lie on the axes to the same extent as eachother, so experience the same overall repulsion from the ligands.

I'm only a first year so any corrections would be very welcome.

The crystal field splitting is based on where the ligands (modelled as point charges) are in relation to the orbitals. In an octahedral complex, the ligands are all at 90° from each other and are placed on each of the x,y,z axes. The orbitals that lie on these axes will experience the most repulsion and will rise in energy, while the orbitals between the axes ($\ce{t_{2g}}$) will lower in energy as they experience less repulsion from the ligands, and the average overall energy is maintained.

I can only assume that the degree by which the $\ce{e_g}$ orbitals are raised is the same due to the $\ce{d_{z^2}}$ orbital technically being a linear combination of what would have been the $\ce{d_{z^2-x^2}}$ and $\ce{d_{z^2-y^2}}$ orbitals. This means that the $\ce{e_g}$ orbitals lie on the axes to the same extent as each other, so experience the same overall repulsion from the ligands.