Say the scenario is you have some strong acid on you, like HCl.
You don't want to use a similarly strong base because you won't be adding it in stoichiometric ratio, you will be adding the base in excess. This implies after 'neutralization', you now have strong base on you, and we're back to the same problem.
For small volumes spilled on skin/other body parts, we tend to just use water to dilute it (that is, running water). This is not because water is amphiprotic, this is simply saying dilute acid is nowhere near as dangerous as concentrated acid. You won't be using powdered substance (for instance, you won't rub NaHCO3 powder on your arm if you spilled some acid. You run it under water to wash it off, then see a doctor if a horrible rash persists)
For larger spills on the ground, like breaking a large beaker/jar full of concentrated acid or base, you would use the amphoteric powder NaHCO3 (weakly basic) to cover the spill, safely neutralizing any acid/base, and gives a convenient method of disposal.
In VCE you don't get to see many strong acids or bases. Conc sulfuric acid would be the only strong chemical you would use, and it is generally handled by a supervisor/teacher, only only in drop-quantity by students. Dealing with 1M solutions or thereabouts is generally low risk (like 1M NaOH or 2M HCl) [that is if your head is screwed on and you don't try to drink any of it]. In the future, you'll learn to use actual safety precautions when dealing with chemicals like 1:1 SO3/H2SO4 (very strong acidic mixture with a lot of acidic vapour) and alkoxides (very strong bases).