Why does slowly decaying ACF indicate that a time series is non-stationary? I am a student studying time series econometric online and looking for help talking around some of the principles. There is one point I am trying to understand better.

I've come across some literature online which talks about how non-stationary data series have slowly decaying ACF. The graph of the ACF of VWAP in this post is a good example: https://coolstatsblog.com/2013/08/07/how-to-use-the-autocorreation-function-acf/

Could someone explain why a slowly decaying ACF is an indication that a series is non stationary? I think hearing an explanation will help me get a better understanding of the material.

Thanks very much,
Adrian
The (simplified) definition of a stationary process is that the mean and variance of the process are constant over time. 

If the ACF is slowly decaying, that means future values of the series are correlated / heavily affected by past values. If past values of the series are high, the future values should also be high. If the value goes up, future values will also go up (assuming positive auto-correlation here). This means the mean will change over time, which means that the process is non-stationary.