아버지 하고 아들

              아이고!!! 너 왜 숙제 안했어?

아들: 안 숙제했어 때문에 못 숙제했어!! (I want this to say: "I didn't do it because I can't do it!")

          숙제를 할수없어서 숙제를 못했어

           or

          숙제가 너무 어려워서 숙제를 못하겠어(It's too hard for me, so I can't do it)

           
아버지: 거짓말쟁이!!! 숙제하세요!!!!

아들: 안 숙제했어 때문에 못 숙제했어!!

I believe you are understanding 안= don't, didn't. It is correct, but the correct sentence will be 숙제 "안"했어 because of grammar issue. As the same as "못 숙제했어" is wrong "숙제 못했어" will be the right sentence 

Tip

숙제를 안하다= Don't do homework by purpose

숙제를 안"했"다= "Didn't" do homework by purpose  

숙제를 못하다= Couldn't finish homework because of an irresistible reason/force.

For me, i don't understand what "I didn't do it because I can't do it!"

Does he has a reason for he can't do his homework?