To me, the theme of this poem (which I first read when I was a senior in high school -- I'm surprised that it amused me back then given the theme) is that young people are not as smart as they think.
The narrator is given all kinds of reasons for not falling in love at that age. But he just ignores them all because he thinks he's too smart to need to listen to the advice. But then, at the end of the poem after he's a whole year older, he knows how true the advice was.
So the theme is that as you grow older you get wiser and that's why I'm amused that I liked it when I was in high school.
The theme of the poem "When I was One and Twenty" is given by the “wise man” in two pieces of wisdom, but they are closely related. One is, in effect, “Don’t give your heart away,” that is, don’t fall in love; the second is, “If you do give your heart away, you will suffer.”
The speaker ignored the advice, and now, at twenty-two, has learned its truth. The last line of the poem, with its repetition, suggests that the speaker takes his youthful sorrow very seriously (“And oh ’tis true, ’tis true”), but surely the line strikes one (and is intended to strike) as a trifle maudlin. And, since the poem jingles nicely and almost suggests a nursery rhyme, we can hardly take the grief too seriously. We listen with sympathetic amusement to this tale of disillusionment, but we are pretty confident that the young man in the poem will survive, and probably will live to love another day.