Short answer: He was just playing tough guy. Quadros' government was a weird mix of reality show, circus and trashcan fire.

Long answer: Since the end of WWI up until the formation of the american dictatorships, a lot of governments in latin america followed the "national-development" policy. The Development part means a powerful State with a strong grip on the economy (including nationalisation of key economical assets) and massive investiments on industrialization, and the National part means a somewhat isolationist policy that disliked foreign intervention. National-development flourished under Getúlio Vargas in the 30's and 40's. Most brazilians politician would try to copy Getúlio in the following decades, Quadros included.

The problem is, when Vargas barred american interference in Brazil, nationalized american assets or condemned american actions, he had the finesse to be diplomatic and never truly cut ties or do something really outrageous. Quadros didn't. A lot of the things he said or did had the objective of getting in the face of the US or Brazil's neighbours, because he wanted to be seen as a strong leader. He tried, both in domestic and international affairs to just strong-arm himself into the position of the mighty president that steers the nation whenever he wants.

The invasion of Guyana was just the last of his ego trips. He also:

• Tried to snuggle up to Cuba in the aftermatch of the Bay of Pigs invasion. That's not bad per se, but he did it when literally everyone around him was warning the presidential cabinet of an imminent and fervently anti-communist military coup.
• Condecorated Che Guevara with the highest Brazilian medal, the Order of the Southern Cross. For some reason.
• Banned bikinis to "defend the nation's morals".
• Banned the Miss Universe contest from being broadcasted in TV, again to defend the nation's morals.
• Brought federal laws regulating the game of cards.
• Cracked down, on a national level, on the greatest enemies of the state... cockfighting rings.

He had some pretty decent propositions too, but they were mostly suggestions from his vice-president, João Goulart. So, yeah, Quadros wasn't the kind of man you take seriously.