All else aside

This noon I got a lesson from my coworker. She IMed me and said my use of "besides" was slightly incorrect. My impression was that "besides", "in addition", and "also" were the same. But, according to her, "also" and "in addition" are close but "besides" is different from the rest. She used the following examples to help me understand the use of "besides": example 1 - I will pick you up tonight. Besides, your home is on the way to the airport; example 2 - I will not join you for the dinner since I have something to do. Besides, I am not even hungry. She told me to think "all else aside". The examples always have two statements. A first and B second. B is a "all else aside" kind statement. No matter will A be happening, B will be always happening. Got it?