但 pairs a person 亻 with 旦 — the sun rising over the horizon (a picture of dawn: 日 above a line of earth). Originally it meant 'only, merely'; the sense drifted to the great turning-word: but.
但是 is the hinge of every Chinese argument — everything before it is politeness, everything after it is the point. 我很想去，但是没时间 ('I'd love to go, BUT no time'). Chinese rhetorical style often grants your view generously first, then pivots on 但是. Master the pivot and you argue like a native; miss it and you only hear the polite half.
A person 亻 watching dawn 旦 — the day turns, the sentence turns: BUT.
In speech, everything before 但是 is often just cushioning — listen for what comes after the 'but'.