Felicity was extra gullible on the "Dangerous Liaison" episode of Arrow. While everyone on Team Arrow has gone through a regrettable phase at one point or another, Felicity working with the vigilante hacking group Helix has to be one of the worst.
Felicity showed her Helix friend, Alena, how to hack into A.R.G.U.S. Armed with the new information, Alena immediately hacked into an elevator and killed an A.R.G.U.S. agent for his keycard.
When Felicity confronted Alena about it her friend said it was an accident and that she was just trying to free Helix's leader, Cayden James. Since James was illegally being help by A.R.G.U.S. Felicity was cool with the kill -- I mean accidents happen.
The rest of Team Arrow told Felicity that she was making a mistake but she insisted that James would lead them to their main target, Adrian Chase. But in a move that surprised nobody except Felicity, it appears Helix double crossed her and tried to blow her up.