I agree with you, Oddly.
People with tattoos talk about the amazing artistry involved, and yes, some of it can look like it's done by a talented person, but for someone who doesn't see the appeal of tattoos, that is somehow rendered meaningless, because tattoos on human skin almost always look generic. They look like tattoos. Similar to the discussion upthread about sleeves - tattoo lovers think they're all unique; non-devotees just think they look like the same old tattooed arm that everyone else has. And the very nature of it being a 'sleeve' means it's going to date to this era, regardless of the intricacies of each person's individual design.
For me, as well, it's about the incongruity of doing this sort of outré thing, that marks you out as an individual, with your own style ... and yet you're stuck with it forever, in a way you wouldn't stick with anything else so publicly obvious - clothes, hairstyles, design, home decor, music - anything.
And it's on your skin for the world to see - therefore people will have an opinion. Not of you, per se, necessarily, but of the phenomenon. Most people won't share that opinion with you, but in the age of the Internet, when anonymous discussion is the main currency, you will be privy to opinions you don't like. People were always thinking them; they just weren't expressing them.