I, too, dislike it. (line 1)
The speaker's sentiments here are pretty clear: she doesn't like poetry. However, she's not the only one; the inclusion of "too" suggests that disliking poetry is a shared feeling.
with a perfect contempt for it (line 2)
This phrase reconfirms the speaker's dislike of poetry, but it also suggests that the speaker looks down on it. She doesn't abhor or fear poetry, and she doesn't try to avoid it. She continues reading it, but with a certain disdain. Describing her contempt as "perfect" also implies that her reservations about poetry will be hard to overcome.