Two time series that are not related can have a strong, but spurious, correlation when a trend is added. This strong correlation is just the fact that they're both dependent on the time (X)
They both increase over time in the period you’re looking at. This is sometimes called secular trend.
See also: Statistics - Correlation does not imply causation
In exploring relationships between two time series, you really want to know whether variations in one series are correlated with variations in another. Therefore trend should be removed.