Explanation: When we talk about a melody-first songwriting process, we assume that we’re talking about writing a song where thinking up the melody, or at least a bit of a melody, is the first step. Then once we’ve got a good chunk of that working and sounding good, we then try to figure out what kind of chords are going to support it.
In fact, that’s not exactly the case. Any good musician (songwriter or otherwise) would find it next to impossible — and I might even say undesirable — to work on a melody without having any kind of notion what the supporting chords are. So in fact, a melody-first process means a melody and chords process.