B). A systematic defens.
As per the question, the option that does exemplify a reason for which Wordsworth wrote 'Preface to lyric poetry' is option B 'a systematic defens'. 'Preface to Lyrical Ballads' marked the beginning of the romantic era in literature which was a reaction against the rationalization and reason of the 'Augustan era' that blindly imitated the classical notions without paying heed to individual emotion or freedom.
There were several reasons for writing "Preface to Lyrical Ballads" like presenting the essential characteristics of poetry(manifesto of Wordsworth's poetic diction) and provide an introduction to lyric poetry . Thus, option B is the correct answer as it has no affiliation to writing 'Preface to Lyrical Ballads'.
the anecdote makes readers feel sorry for the man’s lack of heritage, then reminds readers that the man has an equally valuable heritage.