An idea may strike you as being logical or otherwise, and as far as you are appealing to your own logical intuition, good luck. If you want to go beyond your own intuition, you would have to move through a stage of formalisation, and if, a big if, your formalisation is compelling, and the idea, formalised, turns out to be, let's say, a conjunction of a proposition and its negation, then, certainly, by this formalisation, the idea is now, supra-intuitively demonstrated to be illogical. However, you would have to argue independently for that formalisation, which is not an easy matter. Of course, if you think highly enough of your logical intuition, you will not need to dirty your hands with such public matters as outright formalisation.
On a more serious note, in my experience, a lot of people over-rate their logical intuition, which is often easy to demonstrate, once you lure them out from their intuitive castles in the air. Moreover, what strikes you as an intutively illogical idea, could, and I would contend, often IS a token of your misunderstanding.
I've had it up to here, with wannabee logicians who haven't even bothered to learn the rules of the game. Let's meet on the formal plane and see what shows up!
J