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St. Joseph is the terror of Demons because all of demons effort is nullified if one seeks refuge to St. Joseph and also because he is pure, and demons cannot stand against his purity.
Even though there is no official dogmatic pronunciation in this regard by the Catholic church, numerous private revelationsexample and traditions have held that St. Joseph, after his conception, was, through the future merits of Jesus cleansed from the stain of original sin. And also Catholic tradition holds that St. Joseph did not sin all thru his life.ref Satan and his cohort of fallen angels had no success in seducing Joseph. These are not dogmas however and Catholics are not obliged to believe these traditions.
Catholic Online says about why St.Joseph is the Terror of demons:
Those who turn to Saint Joseph for his powerful intercession and good example do much to keep Satan and the other wholly corrupt devils at bay. In this sense, Joseph is the Terror of Demons because when the friends of Jesus avail themselves of his salutary influence, Saint Joseph is for them a sure protection against the oppressive wiles of the Prince of Darkness. src
One more POV in this regard:
But evil shrinks from Joseph for He is pure. ... The demons can't "see" Joseph because he is pure. Purity makes him invisible, just as pure water is perfectly clear. Evil spirits don't know when, how, or from which direction Joseph is going to hammer them. Joseph's job, when Christ was a child and up to this very day, is to protect the Holy Family, and through our baptisms, we are part of his family. src