Greenpeace is not against purse-seining, which may surprise some people. Sure it's a big industrial-looking fishing operation, involving huge nets and catching lots of fish. But that's not always a bad thing.
If we are to assume we're still going to catch and eat fish, then purse-seining as a method is probably going to be something that continues. Purse-seining involves setting a large circular wall of net around fish, then 'pursing' the bottom together to capture them. Where purse-seining is best used is with large single-species schools of fish, that shoal tightly together. Examples like herring or mackerel spring to mind. These can be caught relatively 'cleanly' by purse-seining.
But where purse-seining is a bad idea is when targeting fish that a) also involves the bycatch of non-target species, and b) simply can't take the fishing pressure on their populations.
And that's where we get to tuna. At both ends of the tuna size and value scale, purse-seining is employed.
For skipjack, the smallest species and staple of tinned tuna, purse-seining is used throughout the Indian and Pacific oceans. The problem here is that skipjack tuna often shoal together with young bigeye or yellowfin tuna. These often end up in the nets too. As do sharks, rays, turtles, and other species of fish. Then when you add in the complicating factor of fish aggregation devices (FADs) - the use of which increases the amount of bycatch - then the problem gets even worse.
The solution here is firstly to stop using FADs, thereby immediately reducing the amount of other species 'accidentally' caught. Then to employ measures to further reduce, and wherever possible free, unwanted species caught up in nets. Given the endangered species of oceanic turtles, sharks, and bigeye tuna, this is not wishful thinking. Cleaning up skipjack purse-seine fishing must happen, and happen soon.
Then at the other end of the scale, massive bluefin tuna are also caught by purse-seines, in places like the Mediterranean. This is by no means a traditional fishing method, and in fact the increase in purse seining over the past few decades has been at the expense of local, traditional methods of fishing that have existed much longer.
What happens today is that the bluefin, aggregating to spawn, are targeted by vast purse-seine nets. Then those that are too young to sell on are towed off to be kept and fattened up in cages.
The Atlantic bluefin population simply can't take fishing at this level. It is this fishing method, and the associated ranching, all in turn driven by a new-found appetite for bluefin sushi around the world (and especially Japan) that have caused Atlantic bluefin numbers to plummet.
They are now an endangered species, and purse-seining rhinos or tigers would be equally reprehensible.
The losers in this set-up, aside from the bluefin themselves, or the bycatch in skipjack nets, are the traditional fishing communities who have been catching these fish with minimal impact for centuries.