Because anyone coming over into the Americas would leave linguistic, cultural, political, and epidemiological evidence. The fact that stuff changed when the Europeans actually did arrive in force shows us what should be there in the case of pre-Columbian contact -- and it isn't. Color me crazy for saying so, but absence of evidence is, in this case, evidence of absence.
Keywords here being "in force". I was not speaking of conquista or migration of entire nations here. Nor about permanent trade routes or embassies. A stray fleet of few ships and few hundred men, perhaps.
And there is evidence which suggests this could have happened. Dozens(?) of (para)historians, some completely crazy, some not so much, have scraped together every semblance of evidence they can find to prove their pet theories about how this contact happened. Few from the top of my head: Pyramids in both Mexico and Egypt; Aztec legends of white, bearded gods from the east, Giant Olmec Stone Heads having Negro faces, boats of Papyrus built on both Lake Titicaca and River Nile... this could go on. Of course, one can pretty easily discard them all, but don't say there is not stuff that can be taken for the kind of evidence you claim is lacking. And for my kind of scenario, what evidence could we hope for anyway? A giant obelisk on Yucatan shore with Egyptian hieroglyphs stating "Admiral Amon landed here on the 12th year of rule of blessed Queen Hatsepsut?"
It has been proven that an adequate technology to cross oceans was there. For me, it is not too big a stretch of imagination to believe that it actually happened at least once or twice within a gap of few thousand years.
EDIT: I was thinking that the only one of your arguments (linguistic, political, cultural...) that actually holds water is lack of epidemiological evidence. However, it occurred to me that viruses and bacteria do change terribly fast - and if they are especially deadly, they kind of "burn themselves out", killing people faster than they can pass them on. So if there had been a contact e.g. in 2000 BC, it shouldn't be a given that whatever germs might have been brought over would really have survived and/or provided immunity/protections against strains that had evolved separately for another 3500 years. Or maybe I am just clueless about epidemiology here.