The Pirate Party MEP is parliament's rapporteur on the review of the 2001 copyright directive, and has advocated for the harmonisation of copyright exceptions and for more power to be given to authors when negotiating with publishers.
Speaking at a press conference, she said, "we need to grant people the same rights online as they have offline".
She explained that research has shown that "a strict copyright protection system does not lead to creation", and that "the main arguments against [her report] were very much linked to unknown consequences".
Reda urged Europe to "show what great creative potential it has, and that people are using the internet in a positive way, to bring culture out there but also to make a living out of creative work through the internet".
Commenting on parliament's reaction to her report, she explained that "opinions are really decided by individuals rather than groups", but was optimistic as to the outcome of the talks, as, "two out of three opinion committees have managed to adopt an opinion and both include many encouraging signs".
She claimed that "fears were more about the fact that I am a member of the Pirate Party and not so much the content of the report".
Speaking alongside the deputy were authors Cory Doctorow and Neil Jomunsi and filmmaker Lexi Alexander.
Doctorow pointed out that "it is important to recognise that copyright is a technological regulation", adding that, "as technology changes, so too does who copyright benefits and serves".
In his view, an effective copyright system is not one where most of the money "is siphoned off by investors, it is one where creators are first in line to get money". Yet today's system "does as much as it can to keep creators away from money".
He explained that due to large companies' dominance, it was getting increasingly difficult for independent firms to compete, saying, "there can be no other Youtubes, except Youtubes started by companies as big as Google", that can afford to invest substantial amounts of money into their projects.
He stressed that "none of [the current copyright legislation] is reducing piracy - we are paying terrible penalties in terms of infrastructure of the internet, and doing very little to protect artists' incomes".
Complaining about geoblocking and the territoriality of copyright laws, Doctorow told the audience, "the last thing I want to know is that in countries [across Europe] there are people who want to give me their money and are not allowed to do so because of copyright".
He lamented that "the current system is about revenue maximisation for the rich at the expense of everyone else".
Commenting on Reda's report, filmmaker Lexi Alexander said, "it doesn't go far enough - I would want it to be much more aggressive".
Yet she did point out that "there are many people opposing this report who say they represent artists, but this is a myth".
She claimed that while many famous Hollywood directors agree that copyright rules must be amended, "many of them are not crazy enough to say it out loud for fear that they will lose funding if they speak up".
In writer and former publisher Neil Jomunsi's view, opposition to the report "is a way of scaremongering and concealing the real problems; essentially the issue is one of fear - publishers and editors are afraid of overwhelming cultural diversity and they are scared they will lose revenue".
He underlined that "the internet and the free dissemination of the arts is a huge opportunity" and that "the current system does not benefit artists, and for a long time it has not worked in their interests".