Please note, I do not necessarily believe in its existence, just after a scientific (hence, non-Wikipedia) reasoning to doubt the planet's existence, other than the "we would have seen it" argument. I am, nor are the articles below, referring to the alleged 'Nemesis' planet, as in the question What are the current observational constraints on the existence of Nemesis?
According to the article Astronomers Doubt Giant Planet 'Tyche' Exists in Our Solar System (Wolchover, 2011), the planet Tyche is a hypothesised massive planet
by John Matese and Daniel Whitmire of the University of Lousiana-Lafayette, is not new: They have been making a case for Tyche since 1999, suggesting that the giant planet's presence in a far-flung region of the solar system called the Oort cloud would explain the unusual orbital paths of some comets that originate there.
Further information is found in the scientists' research paper Persistent Evidence of a Jovian Mass Solar Companion in the Oort Cloud (Matese and Whitmire, 2010), describe the hypothesised planet to be
of mass 1 − 4 M(Jupiter) orbiting in the innermost region of the outer Oort cloud. Our most restrictive prediction is that the orientation angles of the orbit normal in galactic coordinates are centered on , the galactic longitude of the ascending node = 319 and i, the galactic inclination = 103 (or the opposite direction) with an uncertainty in the normal direction subtending 2% of the sky.
They posit that the elongated orbit of Sedna is a result of the presence of this planet.
So, the question, what reason is there to doubt the existence of Tyche?