can you explain bit more about what you really want to do? on the expected result you mentioned closeS2, is it when S1 is still in close? or only one switch is closed at a time? or you are trying to make a memory for the keys pressed and it will be the input to tell ODD or EVEN?
you have used the latches that "set" on input "L" and "LL" is not permissible. if you want other way then use an inversion before the inputs.
Edit:
1) i made a mistake, the latches are set by logic high, but the output goes low that time, by swapping the outputs you will get the right result. or you have to invert the out puts.
2) the reset input is not having any value like floating, it might have caused a problem in your result.
3) when the key is pressed the output changes/ toggles that is an input to your latch, so you may get different result depends on semiconductor response time. you better use a D-flip flop before connecting.