The actual thing they get tattooed is "I refuse to sink". It's a thing, okay? To me it means that even though you may have things weighing you down (i.e. an anchor), you refuse to let it over-take you completely....
Friend of mine has this and says it's the idea that the anchor should sink but is fighting against what it should do to do what it wants to do. Being individual kind of thing
Ugh, I want to strangle people with those tattoos. How does that make any sense? Just get either on or have them on separate parts of the body so it doesn't make no sense.