I am male, dont bother right or left. But my wife prefers left.
In certain yogic text they say right side is for female and left is for male. In HATHA, HA is male, THA is female (please notice THA contains HA as in woman/man, female/male, she/he). So when you face HATHA, HA is in left and THA on right.
Also there is a hindu god called Ardanari with male half on left and female half on right side (when you face the god). A very meaningful symbolism. Sorry if it is very irrelevant here.
