There's two things going on that explain why your answer is insufficient. First,
I'll start with an apparent wording problem in your answer:
Both conclusions cannot be true and valid as it’s not possible to do and not do the same thing
If I'm understanding, your sentence correctly you seem to be saying:
both conclusions cannot be true
both conclusions cannot be valid
It might just be a fault of wording, but the second claim is incorrect. Validity is a concept that applies to arguments -- not conclusions. It's possible you're getting the answer wrong because of this somewhat nit-picking problem.
Now on to the answer as to why at least one of these arguments must be invalid.
First, we need a definition for reference: validity means that if the premises were to be true, then the conclusion must also be true.
Second, I'm not quite sure what "pieces of reasoning" are. I'm going to assume that means arguments.
Third, it is possible for contradictory conclusions to be reached by valid arguments. This is true because validity only looks at the logical relationship between the premises and conclusion. Thus, we could conceivably have two valid arguments with the conclusions Oswald shot Kennedy and Oswald did not shoot Kennedy. (Thus, the explanation you provide is wrong (or at least horribly unclear) -- because contradictory conclusions means nothing).
What matters here is what happens when we apply the definition of validity to each argument in conjunction with the stipulation that the sets of premises for each are true. Let's say the shot argument is argument A. The did not shoot argument is argument B.
We can construct the following argument:
- If A is valid and A's premise is true, then Oswald did shoot
- If B is valid and B's premise is true, then Oswald did not shoot
- A's premise is true [given]
- B's premise is true [given]
- | A is valid (assumption of sub-argument)
- | A is valid and A's premise is true [&I5,3]
- | Oswald did shoot [MP 1,6]
- | ~ [B is valid and B's premise is true] [MT 2,7]
- | Either B is not valid or B's premise is not true [DeM 8]
- | B is not valid [DS 9,4]
- Ergo, if A is valid, B is not valid
Then repeat 5-10 for the assumption B is valid as a proof that if B is valid, then A is not valid.
This may be what you meant to say with your sentence, but it's not clear enough. A clearer wording is that their conclusions are incompossible and the premises are true, so at least one argument must not be valid since if both were valid both conclusions would follow necessarily.