Often the future continuous is a way to soften a committment. 'I will show you' sounds like one should be asking 'when?' whereas 'I'll be showing you' feels assuring, like we will get to it even if the specifics are now vague.

I will show you is future simple. It doesn’t imply it’ll go on. But I will be showing you is inferring that it’s a future action that’ll be going on.

Hi Okay so, The future continuous tense, is a verb tense that indicates that something will occur in the future and continue for an expected length of time. so if you say I will show you. its more like a one time thing. Where as if you say, I will be showing you, it is stating a more continuous thing that will be happening continuously in the future. I know it may be confusing so if you still don't understand please message me.