She is after a long-term relationship, not a hookup. I imagine the idea is that catching fish with nets is different from and more permanent than fishing with a line and hook and then throwing the fish back in the lake, hence the fishnet stockings. But the analogy doesn’t work for long as generally those net-caught fish are eaten or made into catfood or something. Not many people go fishing (for fish) to get a permanent pet.
If the stockings are held up by garters, there is also some catch-and-release involved in that mechanism. This is maybe an additional fit, in general I agree with narmitaj that she is using (perhaps not quite consciously?) fishing method metaphors to announce her coupling policy.
I think there is also a joke about people using obscure signals that they think everyone should immediately understand.
Initially I understood the reasoning exactly as narmitaj explained it @1, but when reading it later my brain made a retrograde connection: aren’t “fishnet stockings” a common part of a “hooker’s” attire?
Narmitaj @1: but fishing is a common and long-standing metaphor for finding a romantic partner; the fact that one typically doesn’t fillet, cook and eat romantic partners can hardly be held against this comic.
Dude, let her go. There are other fish in the sea.
Perhaps when she ended her catch-and-release days, she took her fishnet and turned it into stockings.
Comics I Don't Understand 
She is after a long-term relationship, not a hookup. I imagine the idea is that catching fish with nets is different from and more permanent than fishing with a line and hook and then throwing the fish back in the lake, hence the fishnet stockings. But the analogy doesn’t work for long as generally those net-caught fish are eaten or made into catfood or something. Not many people go fishing (for fish) to get a permanent pet.
If the stockings are held up by garters, there is also some catch-and-release involved in that mechanism. This is maybe an additional fit, in general I agree with narmitaj that she is using (perhaps not quite consciously?) fishing method metaphors to announce her coupling policy.
I think there is also a joke about people using obscure signals that they think everyone should immediately understand.
Initially I understood the reasoning exactly as narmitaj explained it @1, but when reading it later my brain made a retrograde connection: aren’t “fishnet stockings” a common part of a “hooker’s” attire?
Narmitaj @1: but fishing is a common and long-standing metaphor for finding a romantic partner; the fact that one typically doesn’t fillet, cook and eat romantic partners can hardly be held against this comic.
Dude, let her go. There are other fish in the sea.
Perhaps when she ended her catch-and-release days, she took her fishnet and turned it into stockings.