Well yellow it depends how you pack really, if you do just move clothes to another place then yes it's probably irrelevant who does it.
But if like me you enjoy writing lists beforehand, laying everything out, working out which activities you will be doing etc, have very good 'non creasing' folding skills, don't want to go out to nice restaurants with DP looking like he is wearing a brown paper bag and smelling rancid because he thinks it's fine to recycle socks and pants in 32 degree heat, AND most importantly enjoy it.
Compared to DP who has shocking spacial awareness and a sense of logic which genuinely leaves others bewildered so will stuff white shirts in the bottom of the bag and put muddy boots on top.
You may say well let him smell and have mud over his clothes, but i really don't want to. Also you may say well then he would learn. But he doesn't. Because being the way he is, looking and smelling like that doesn't bother him. (he is savantish in his ways and has been told he is on the aspergers spectrum)
And i do think packing is a skill (not necessarily a feminine one either). I know more men who precision pack and women who shove it all in a rucksack.