If a problem is "not semi-decidable" and "not decidable" can we say it is "undecidable"? I was under impression that when a Language (or problem) is not semi-decidable and not decidable then we can say it's undecidable and I think it makes sense also based on diagram. 



However, in my assignment the TA struck out "undecidable" and wrote "not semi-decidable". Why is "undecidable" wrong if it's both not semi-decidable and not decidable?
Undecidable isn't wrong: "undecidable" means exactly the same thing as "not decidable". However, your TA is saying that you can make the strictly stronger statement that the set is not even semi-decidable.  This implies that it's undecidable, but isn't implied by "it is undecidable".

Suppose you were, instead in a biology class. You wrote "This is not a lizard" and your TA crossed it out and wrote "This is not any kind of reptile." You're both right, but your TA's version has more information in it.