For the major case for application of the "Always Add Acid" rule, the reasons are obvious. Adding water to concentrated sulfuric acid usually leads to local overheating of water. That causes local violent boiling and splashes of concentrated acid. That is avoided by adding the acid to water as there is a lot of heat capacity to avoid boiling.
From personal experience, it is good to do it in two steps, if applicable, as it is less challenging, considering cooling and manipulation with hot acid solutions.
- Pouring the rest of the older diluted acid to water and cooling it down.
- Pouring the concentrated acid to this new mixture.
When concentrated sulfuric acid and $\text{30+ %}$ hydrogen peroxide are to be mixed, it is choosing the smaller evil of pouring the hydrogen peroxide to the acid. This still can cause eventual smaller splashes of the acid or surface hydrogen peroxide decomposition. But it avoids local overheating and dehydrating of hydrogen peroxide solution. That could destabilize it and making it violently decompose in the whole volume, splashing most of the liquid.
Note that sulfuric acid has kinetically stabilization effect due acidic environment and at the same time destabilization effect by heating up and bonding with water. That latter increases the thermodynamic activity of the peroxide.
Preparation and manipulation of this piranha solution is always dangerous and should be reserved to experienced chemists, considering all needed precautions. It is not called so without a reason.