There Is No Logical Reason
Sometimes, it goes like this: "There is no logical reason to do-some-thing-the-speaker-disapproves-of", like, buy full-fat versions of a product right next to a low or no fat version of same.
Sometimes, it goes like this. Actually, I would argue it goes like this more often than any other way: "There is no logical reason to believe in god."
Once in a while, it goes like this, quoting Rebecca West (http://www.notable-quotes.com/w/west_rebecca.html): "There is no logical reason why the camel of great art should pass through the needle of mob intelligence."
You should always be allowed to quote Rebecca West, so I guess it's okay to say "There is no logical reason why" in that one case. Possibly others similarly.
But as I google "There is no logical reason why" in quotes, and even "logical reason" in quotes, I have to say I have no mortal clue what these things might mean. Possibly, they are an expression of contempt for the values of people so different from oneself that it just doesn't seem worth bothering to figure out why they are doing or thinking whatever they are doing or thinking. Possibly, it is an expression of contempt for those values after having bothered to figure out why they are doing or thinking whatever they are doing or thinking and concluding that Those Are Not Good Reasons.
Possibly, it is an expression of ignorance that is risible -- you might want to avoid that, especially if you are projecting your ignorance, by asserting that something couldn't possibly be so, just because your imagination has failed to encompass the possibilities of reality. All those people who talked about Junk DNA, just because a bunch of DNA didn't directly code for proteins, are feeling Pretty Stupid right now. Don't be Them.
But if you are saying "logical reason" to mean, Hey, I think you care about stupid, irrelevant shit that I do not care about, I'd really find it a lot more logical and reasonable if you said that, rather than trying to encapsulate it in "logical reason". Because I'm not actually certain there is such a thing as "logical reason". There are reasons. There is logic. Not so sure about the combination.
ETA: "There is no logical reason why", "There is no good reason why", "There is no valid reason why" and "There is no reason why" are all used roughly similarly (and are all approximately equally problematic), altho I will note that they tend to be used by different groups of people, if judged by the rest of the assertions often associated with them. And this has been going on for a while, cf _The Foundations of Empirical Knowledge_ by one Alfred J. Ayer, 1963 (stumbled upon via google). No, Ayer did not analyze these constructions. He perpetrated at least two of them ("logical" and "valid").
R. notes the passive voice.