# Removing seasonality in time series forecasting

In time series forecasting we are removing the "seasonal" component to fit models better and have better forecasting. But why? if I should give an extreme example: if I have a sin wave, I wouldn't remove the seasonal component of it. Because it is much easier to forecast with its own structure (because it has an easily recognizable pattern). Am I wrong?

$$\psi(t) = \psi_s(t) + \psi_\tau(t) + \varepsilon(t)\, .$$
In order to forecast the future behaviour the only "unmodelled" part is the $$\varepsilon$$ component, hence you already know how to forecast the trend and seasonality parts. So, a first forecast model might be created by decomposing the series and model trend and seasonality.
This, however, comes from the chosen model, meaning your hypothesis is that your time series is actually decomposable as above (with $$\varepsilon$$ following a normal distribution).