I, too, dislike it. (line 1)
The "too" here suggests that the speaker empathizes with another person, or group of people, who dislike poetry. The speaker isn't just spontaneously declaring her own opinion; she is responding to a prevailing opinion or feeling.
Reading it, however, with a perfect contempt for it, one discovers (line 2)
When the speaker began the first sentence with "I," she quickly added a "too" to indicate her membership in a larger group. In the second sentence, the speaker delays using any noun at all, leaving who is reading poetry and who has a perfect contempt for it ambiguous. When she finally introduces a noun, it is the impersonal and all-encompassing "one."