Orgoglio is a real low point for Redcrosse in Book 1. He's unfaithful to Una with Duessa, then is unable to actually fight this giant, and ends up rotting in a prison in Orgoglio's castle while Duessa take up with the Giant. Ouch.
Orgoglio, a massive, club-wielding tyrant, is like Lucifera, a kind of worse-case-scenario vision of leadership. Giants have a general bad rep in the Bible (Goliath ring any bells?) and in Classical mythology, where they're associated with the Titans who refused to obey the leadership of Zeus.
You might be noticing a pride-trend here: Orgoglio's name is derived from the root of "pride." Orgoglio is further linked to very negative Biblical imagery when he gives his new girlfriend Duessa a cute little seven-headed beast to ride everywhere, making her look exactly like the Whore of Babylon. Together the two suggest a state of being defined by defiance of God and of the Church, which Redcrosse comes to represent. For a book dedicated to Holiness, this is an understandable low.