Imagine you're on a snowmachine 10 feet south of the North Pole pointing due east. I tell you to ride for 10 miles without turning. You don't need to worry about map projections or anything - just don't turn. When you stop, are you still 10 feet south of the North Pole? Clearly not, you'll be about 10 miles south of the pole.

It's exactly the same if you start in Seattle. If you drive for 10 miles without turning, when you stop you will no longer be at Seattle's latitude - you'll have gone south.