It's explained quite clearly in the song. The Girl is asking him a series of loaded questions thusly: [Girl] After awhile you'll forget everything. It was a brief interlude And a midsummer night's fling, And you'll see that it's time to move on. [Boy] I won't do that. I won't do that. [Girl} I know the territory, I've been around, It'll all turn to dust and will all fall down, Sooner or later, you'll be screwing around. [Boy] I won't do that. No, I won't do that. So what he means is he won't cheat on her. Thread over
still think the original lyric was 'scat' and the authorities made him change it to 'that' just sayin