What is the practical reason for associating cut-off frequency to %50 power attenuation?
First, calling it the "cutoff frequency" leads to misconceptions.  "Rolloff frequency" is a better name that gives you a more accurate mental picture of what is really happening.

Using the -3 dB point is not arbitrary.  It falls out from the math naturally.  For a R-C filter:

&nbsp;&nbsp;&omega; = 1 / RC

where &omega; is the frequency in radians/second, R is in Ohms, and C in Farads.  For the frequency in Hz, use:

&nbsp;&nbsp;f = 1 / 2\$\pi\$RC

If you plot the Log(amplitude) as a function of Log(frequency), such as in a Bode plot, then the -3 dB frequency is where the asymptotes for the pass band and stop band meet.  Put another way, at frequencies well into the pass band, the filter looks like a horizontal line.  At frequencies well into the stop band, the filter is a line with a slope of 20 dB per decade (+ or - depending on high or low pass).  If you draw those two lines and extend them to where they meet, it will be at the -3 dB rolloff frequency.