"forgive me" is not a proper translation, it should be "excuse me"? Really?
Dictionary guves excuse me and sorry, but we dont say excuse me uf you cant do sinethibg because you have other plans. You say excuse me if you get in 'someones way or interrupt them, so it shouldnt be an alternate translation. You usually say sorry, but i have other plans. If its a close friend i coukd see saying forgive me, si that shoukd be the alternate here.
Personal opinion. I use ЗАТО in more positive light after answering a negative sentence.
For example: ОН ТОЛСТЫЙ, ЗАТО ОН СИЛЬНЫЙ. HE IS FAT, BUT HE IS STRONG.
НО is a general use for BUT, and I often use it in negative way after positive response.
For instance: ОН ТОЛСТЫЙ, НО НЕ ЗНАЕТ СУМО. HE IS FAT, BUT DOES NOT KNOW SUMO.
Odd...I was taught that ‘простите’ means ‘I am sorry’ where as ‘извините’ only means ‘excuse me’, and I made the conclusion that ‘простите’ is more formal than ‘извините’ since ‘I am sorry’ sound more formal to me than ‘excuse me.’ This I was taught by RussianPod101: https://goo.gl/s5CnwA.