Lyric discussion by Atman 

This song has a introductory section, which was a common practice in Broadway and Tin Pan Alley songs. So even though it is a pop tune, it harkens back to an earlier form. Both Lennon and McCartney used it for many songs. (Check out "Misery" and "Here There and Everywhere")

Lennon is expressing the hope to his new love that theirs will be a more mature relationship, not just the youthful infatuation of his previous one. He has found that love is more than "just holding hands," and has moved beyond it, apparently unlike his last girlfriend. So he's saying lets not start this unless you are sure and ready to be in a serious, adult relationship. The sentiment strikes a strong chord to someone between 18 to 21 who is moving from the "childhood sweethearts" phase and considering the consequences of a serious relationship.

You have to be a musician to appreciate how complex this song is. Lennon and McCartney switch singing lead and harmony at various points, because Lennon had a better lower range and McCartney had a better higher one. As a consequence, you have to be a very good singer with a wide singing range to cover it. Also, the chord progression goes unexpectedly to a minor key and then back. It sort of supports the feeling of cautious optimism in the song and the regret and sadness over the previous lover mentioned.

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