Should I continue with daisy chaining?
The danger is that you could plug in enough devices to overload the wall socket. Your dad is probably right, but to make sure you should add up the Watt or VA ratings of each device you have. If the total is less than the rating of the wall socket (and power strips) then you should be OK.

Some devices may be rated in VA or Watts, while others may only specify Amps. To convert from one to the other use the formula Watts = Volts x Amps, and its inverse Amps = Watts / Volts. Volts is the voltage of your mains (eg. 115V or 230V).

If you have some higher power devices and others that are lower power, try to plug the higher power devices into the strip closest to the wall socket. This will reduce voltage drop through the power strips. Some power strips are not very well made and may have loose sockets which get hot at high current. Obviously the fewer plugs and sockets the current has to go through, the less likely this is to be a problem.