Why does slowing down audio introduce aliasing?
That's because you are interpolating the signal. Take a look at this figure:



This is zero interpolation, i.e. inserting zeros between samples, but applies to your case too. The replicas at 2*pi are distorting your signal. You can see them in the third graph, at -2pi/L, +2pi/L. So, you need a low pass filter with a cut off frequency pi/L, after expander. 

In your case, the expander's output dtft will be X(w*2) + exp(-jw)*X(w*2), assuming input signal's dtft X(w). So, your extrapolator output will look a bit different, but the idea is the same.