Alternate means every other row. When you have to bind off stitches, you can't do that at the end of a row, so you have to do it at the beginning of rows. Yes, it may seem that it's 'off' by a row, but that's the way it's always been done, and the only way it can be done, and it makes no difference.
If you have to decrease at the beginning and end of every alternate row, then you decrease on a row, and then work a row without decreasing. It allows for a more gradual decrease.
Does this clear up your dilemma?