How can you justify that cathode rays originate from the cathode whereas anode rays do not?

Any gas taken in the discharge tube always produces cathode rays having electrons with same mass and charge. These electrons are produced due to their knock out from the atoms present inside the gas.
This shows that the cathode rays must be originating from the cathode which are hitting the atoms of the gas to knock out electrons from them.
Anode rays consist of positively charged particles with mass nearly equal to the mass of the atoms of the gas. These are again produced due to knock out of electrons from the atoms of the gas by cathode lays converting the atoms into positive ions.
Thus, these positive ions are produced in the space between cathode and anode and do not originate from the anode.