Pros: Cable doesn't get snagged when person sitting next to you gets up on the subway, ripping them out of my ears. I can connect them to my phone, tablet, tv easily and move around the house without the device.
There's perfectly valid reason to have wireless headphones.
Even around the house wireless can be an advantage. I don't mind being tethered when I'm at my desk, but I'm not always at my desk and wires running to a phone can be a real nuisance, getting snagged on drawer handles and tempting pet chewing.
I feel like most of the "must be wired" brigade check two boxes
1. Too stubborn to move on from their favorite pair of enthusiast headphones
2. Haven't actually _used_ modern wireless headphones much, if at all.
I love a pair of good Sennheisers, or Audeze, or whatever the new $2000 hotness is these days when I'm sitting at my desk, but when I'm on the go? Give me a pair o f bluetooth headphones 100% of the time. The convenience is beyond worth it IMO.
There's perfectly valid reason to have wireless headphones.