Beatrice, being like a sister to the flowers of the Garden, is the only real inhabitant of the Garden. Having confirmed that Beatrice is as poisonous as she is beautiful, Giovanni becomes enraged at having been tricked into becoming poisonous as well. Beatrice is innocent; she was lonely and fell in love with Giovanni. It was Dr. Rappaccini's plan to lure Giovanni into the garden and to have him fall in love with Beatrice. Beatrice is hurt by Giovanni's insults that her breath and even her prayers are tainted with death. She doesn't yet know that Giovanni is now poisonous as well:
I, it is true, am the horrible thing thou namest me. But thou!--what hast thou to do, save with one other shudder at my hideous misery, to go forth out of the garden and mingle with thy race, and forget that there ever crawled on earth such a monster as poor Beatrice?
Then, Giovanni breaths on some insects. As the insects die, Beatrice realizes that Giovanni is poisonous too. So, Giovanni's irruption has caused its lone inhabitant, Beatrice (not counting the flowers) to defend herself against his insults. She admits to being physically poisonous but spiritually, she is "God's creature" and only wants to be loved. This in turn, leads Giovanni to apologize for his outburst. He offers her the antidote and it kills her. In the end, Beatrice says to him, "Oh, was there not, from the first, more poison in thy nature than in mine?" She is speaking of poison in the metaphorical sense as "hate" or "distrust." Indirectly speaking, it is Giovanni's irruption that was as hatefully poisonous as the physical poison of Beatrice's breath.