Why do my bathroom sink drain into my bathtub

why do my bathroom sink drain into my bathtub
Because the tub's connected to the lavatory drain but the lavatory drain's clogged downstream from the tie in so the waste water comes up in your tub. The solution would be to snake the drain line from the roof vent.
Put out enough cable to reach the base and 20 feet more. Good luck, Tom

You could also remove the overflow plate from the tub and rod down that line.