I went to the link, scrolled down to the 'Discards at Sea' section and read it. I am prepared to change my initial point of view if the evidence is presented but I see nothing in that paragraph that contradicts my initial point.
Yes, fair to say fisherman can not control the species they catch to a fine degree of accuracy, but they can chose to fish where the species they are looking for are likely to be, and should have enough experience to know roughly what amount of other species they are likely to get in the catch.
If the public don't presently want to buy these other species, then in the main that is lack of familiarity and a marketing problem (unless the species caught are simply unpalatable in which case the loss of life is not quota related). That bit is fine and one can support encouraging variety in our diet.
But why would it be that fishermen are not allowed to land them ? As I understand it that only becomes so if the fishermen have deliberately opted to fill their quota of that particular species earlier in the season, and so have only themselves to blame when they go over limit later. It seem to me to be obvious nonsense to say that the fishermen have no choice but to throw them overboard; I'm not that daft, anyone can see if they haven't earlier deliberately fished for the preferred species until their quota was reached, they wouldn't have the problem of being over later.
If HFW can explain how the fishermen are prevented from organising their fishing properly then maybe the petition would be worth signing, But at the moment it seems to be just a case of trying to fool us into supporting the removal of the quota system for the short term benefit of the fishermen and in the long term, a loss of a food source.