Is there a discrepancy between the ratio and total expenditure methods of measuring elasticity?
If something rises by $25\%$ then you then need a $20\%$ reduction in the new larger number to get back where you started: $1.25 \times 0.8=1$. This asymmetry means comparing large percentage changes can produced oddities

Another approach, closer to the idea of approaching the derivative as a limit, is to use logarithms and calculate the elasticity as a ratio of logarithms, something like $$\frac{\log\left(\frac{Q_2}{Q_1}\right)}{\log\left(\frac{P_2}{P_1}\right)}= \frac{\log(Q_2)-\log(Q_1)}{\log(P_2)-\log(P_1)}$$

and with your example this would give $\frac{\log(15)-\log(12)}{\log(8)-\log(10)} = \frac{\log(1.25)}{\log(0.8)} =-1$ as expected