Stay with me because this one is a bit tricky.
As you know, ~어/아서 is a connection to show order with reason.
"Because A happened, B happens" as in:
늦어서 미안해.
Because I'm late, I'm sorry.
But, so does ~으니까/인니까 show cause and effect order with reason.
"Because A happened, B happened" as in:
어제 피자를 먹었으니까 오늘 냉면을 먹자.
Because yesterday I ate pizza, today let's eat noodles.
So, why not flip them? Why can't I say these:
(x) 늦으니까 미안해.
(x) 어제 피자를 먹어서 오늘 냉면을 먹자.
Here's why. If you're asking for a:
favor or a request (blah blah해 주세요),
an order (blah blah 해라/blah blah으세요)
or a suggestion (blah blah을래?/blah blah을까?)
then you use ~으니까. Examples:
추우니까 따뜻한 옷을 입어봐.
Because it's cold, wear warm clothes.
자기야, 비가 오니까 우산을 가져 가요.
Honey, since it's raining take an umbrella with you.
감기 걸렸으니까 푹 쉬세요.
Since you caught a cold, rest well
몸이 안 좋으니까 일찍 가세요
Since you're not feeling well go (home) early.
여러분 금요일이니까 외식 하자!
Everyone, Since it's Friday, let's go out to eat!
시간이 없으니까 우리 택시 타는게 어때?
Since we're running late, should we take a taxi?
제가 외국인이니까 이해 주십시오.
Since I'm a foreigner, please try to understand me
So when does one use ~어/아서? Most commonly when it's an apology. Also, past tense is never reflected in the first verb. One would never say "늦었어서". Instead, "늦어서".
~어/아서 examples:
너무 늦어서 죄송합니다
(lit) Because I'm too late, I'm terribly sorry.
Sorry I'm so late.
연락을 못 드려서 미안해요
(lit) Because I didn't hear your call, I'm sorry.
Sorry I didn't hear your call
늦게 일어나서 밥을 못 먹었어요.
(lit) Because I lately woke up, I could not eat food.
I didn't eat breakfast because I woke up late.
시간이 없어서 숙제 못 했어요.
(lit) Because time did not exist, I could not do my homework.
Because I didn't have enough time, I didn't do my homework.
작년 여름에 한 반도 운동을 못 해서 살이 쪘어요
(lit) Because last year's summer I couldn't exercise not even once, I gained flesh.
I gained some weight because I didn't work out at all last summer.
So, in review:
when suggesting/requesting/ordering someone to do something, use ~으니까
When simply stating cause and effect or offering an apology, use ~어/아서
Bonus! Here's my teacher's response to my question. Her explanation is awesome and should help those still with questions as well as serve as a review.
