The problem is moving from estimating a single hypothesis into few ones.
One could claim that X and Y are symmetric, if we were willing to examine X, why shouldn't we examine Y?
The difference is that since Y wasn't part of the original plan, it is possible that there are many other variables there Y1, Y2, Yn...
Consider that we have extra n variables, all purely random. If we have a large enough n, one of them will have observations that seem to be correlated to F.
In case that you consider a pair of variables, the number of options you have becomes O(n^2).
The more complex hypothesis set you'll have, the more options you will have and more likely you will be to gat a false correlation.
It doesn't mean that you should ignore the result regarding Y. Many discoveries were accidentals.
As Robert de Graaf suggested, you can do another experiment and check the Y-F relation.
You can also check multiple hypothesis techniques in order to evaluate your current results in order to estimate whether the new relation is significant.