Ambiguous definition of Substitution and Income effect? Consider the (schematic) indifference curve diagram of two good-quantities Q1, Q2:


According to Wikipedia we call the vector AB' the substitution effect and the vector B'B as the income effect.

I now wonder why I could not, instead of translating the tangent through B onto the lower indifference curve, translate the tangent through A to the higher indifference curve, thus denoting AA' as the income effect and A'B as the substitution effect.

Note that these two definitions do not coincide for (sufficiently) different shaped indifference curves.
First, you can make any definition you want as long as you use it consistently, but it's usually better to adopt the standard definition if you want to avoid confusion.   Similarly you could ask why we don't call a garage a dogpound and a dogpound a garage.  We perfectly well could, but it's better if we all use words the same way.

Second, assuming we agree to adopt the standard definition, your picture doesn't give enough information to determine a substitution and an income effect.  That depends on where you started and what changed, which you haven't told us.

IF you started at $A$ and the price dropped, then, according to the standard definition, the substitution effect is from $A$ to $B'$ and the income effect is from $B'$ to $B$.

If you started at $B$ and the price rose, then, according to the standard definition, the substitution effect is from $B$ to $A'$ and the income effect is from $A'$ to $A$.

Third, if you want to adopt your alternate definition, you will find that your definition and the standard definition agree arbitrarily closely for sufficiently small changes.  So if you imagine an infinitesimal price change, it doesn't matter which definition you adopt.  But for finite price changes, what matters is not that one definition is better than another, but that we find a definition we can all agree to use.