Not. Yes, that's the right answer. After all, is a dragon illogical? Does it suffer from an undistributed middle? Does it commit argumentum ad misericordiam? A four-term syllogism? An argumentum ad baculum? The answer is no and no and no and no. (It might make an argumentum ad baculum while telling you to leave it alone, or let it eat you, dragons being notorious for stuff like that, but it does not commit one by existing.)
Indeed, nothing can be more illogical than calling a being's mere existence logical or illogical. Were black swans illogical before we discovered them, or does their mere existence ? Are gray swans illogical at the moment? Would they become logical after genetic engineering or spontaneous mutation?
Not to mention magic vs science often pretends that science is intrinsically "rational" and magic intrinsically "irrational". This is seldom if ever justified by their depiction. You could work out something where magic is trafficking with beings from the vasty depths, and depends on placating their whims, but most have a systemic body of knowledge that reliably works, so what is irrational about it?
Or even Star Trek. McCoy is far more logical than Spock. They are generally working in the arena of practical rather than theoretical reasoning, but there's only one of whom whose actions are always consistent with his premises.
There are times when I can only admire the man who observed that there is those who hold Reason in such profound respect that they never bother is actually, like, use it or anything profane like that.