The higher the sidelobes of a signal frequency spectrum, the greater the "cross-talk" between transmission channels Why is that 'The higher the sidelobes, the greater the "cross-talk" between channels' when transmitting signals via hardware electronics? 

where,


Cross-talk:  a signal transmitted on one circuit or channel
of a transmission system creates an undesired effect and/or interference in another
circuit or channel. 
Sidelobes: The sidelobes (spectral leakage) introduced to signal frequency spectrum after
application of window functions to the transmission signal.
Convolution theorem states convolution in time domain is the same as multiplication in Fourier domain, also the multiplication in time domain is a convolution in Fourier domain.

So when you truncate a signal (multiply it by a window), your signal's spectrum will be convoluted with the window's spectrum which widen your signal's spectrum depending on the main lobe width and also replicate signal spectrum depending on the side lobe height which is called frequency leak.
if you consider different channels over different bandwidth, when you truncate the signal the frequency leak will cause channel cross-talk.