On one hand, a reader could legitimately say that the poem's speaker doesn't actually feed his wrath. He waters it with tears and suns it with false smiles and "deceitful wiles." The speaker's wrath is compared with a plant, and plants don't feed, because they produce their own sugar through photosynthesis; however, a poem about a plant grown from anger that produces a poisoned fruit used to kill someone is hardly a poem that should be taken literally. The narrator "feeds" and nurtures his anger by first holding onto it. The speaker admits that his initial anger went away after confessing it. The second bit of anger not only didn't go away, but it also grew because he didn't admit his anger.

I was angry with my friend;

I told my wrath, my wrath did end.

I was angry with my foe:

I told it not, my wrath did grow.

And I water'd it in fears,

Night & morning with my tears:

And I sunned it with smiles,

And with soft deceitful wiles.

In this poem, the persona fed his anger by burying it inside of himself. In the first stanza, he contrasts this approach with his better behavior toward his "friend." When the persona becomes angry at his friend, he discusses it with him and, as a result, gets over it. However, when he grows angry at his foe, or enemy, he doesn't tell him about it.

In addition to not expressing his anger to his enemy, the persona feeds his anger in other ways: he dwells on his anger all the time, never letting it go and in fact, grows more fearful of his foe. As he puts it, he "water'd" his growing fear "night and morning" with his "tears." He also feeds his anger by pretending to be nice to his enemy, all the while inwardly seething. 

The poem expresses how poisonous it is to nurse a grievance and how destructive that can be. 

In "A Poison Tree," to whom did the persona show his true anger, and why do you think this happened?  

In "A Poison Tree," the persona expresses his anger to his friend. He probably feels comfortable talking to his friend about what upsets him because they have a relationship built on mutual trust. The persona most likely assumes that if he told his friend about why he was angry, the friend would not use this information against him. The persona feels safe, in other words, to express his vulnerability. The persona also probably assumes that the friend does not upset him on purpose or out of malice. Most likely, the persona thinks the issue was a misunderstanding that could be resolved through talking it out. Blake shows that he was psychologically astute in understanding how trust works. As we see later in the poem, when the persona reacts quite differently to an enemy, communication is key to resolving differences.