When I was one-and-twenty (1)
We hear that our speaker is 21 three times. That's an awful lot of space in a poem that's only sixteen lines long! Any time that a phrase is repeated so often, chances are that it's pivotal to the work of the poem.
But I was one-and-twenty, No use to talk to me. (7-8)
Silly, silly young lad. This sort of comment is the type that no one could make in the present tense – it's the kind of self-reflection that's just a little bit self-deprecating. Plus, it's just oozing with irony and condescension for the man that he was. Good thing he's changed, huh?
And I am two-and-twenty, And oh, 'tis true, 'tis true. (15-16)
Why call yourself one-and-twenty instead of twenty-one? It's for this line, folks. See, when the big change (his birthday) rolls around, putting the "two" in front of the twenty makes it super-clear that it's the ONE YEAR difference that causes such a huge shift in his perspective. After all, twenty-one looks a lot like twenty-two. But "two-and-twenty"? Everyone can see how different that is!