Why is this tsumego solution wrong?
In tsumegos where you should kill a group, the best (and thus correct) answer is always the solution where you kill unconditionally (if possible). Only if there is no unconditional kill the ko would be the best (correct) solution.

The basic idea is that a tsumego is a local fighting position which you should solve without knowledge of the rest of the board. In your example, the rest of the board could either be that white has more ko threats or that black has more ko threats. Thus, your solution would depend on the unknown rest of the board, whereas the unconditional kill works always.

In general, if there is a position with equal outcome you should always prefer the way without ko. Even if you have more ko threats now, the position might change over time and therefore it is better to avoid the ko from the beginning.