No reason justifies disbelief.

[The Grand Nudger]

They do appear in "fact based" hunting books, from serious people, actually.  That's where the myth as we know it is likely to have originated.  

A number of seals seemingly depicting unicorns have been found from the Indus Valley Civilisation. These have also been interpreted as representations of aurochs—a type of large wild cattle that formerly inhabited Europe, Asia and North Africa—or derivatives of aurochs, because the animal is always shown in profile, indicating there may have supposed to have been another horn, which is not seen.[5]
Unicorns are not found in Greek mythology, but rather in the accounts of natural history, for Greek writers of natural history were convinced of the reality of unicorns, which they believed lived in India, a distant and fabulous realm for them. The earliest description is from Ctesias, who in his book Indika ("On India") described them as wild asses, fleet of foot, having a horn a cubit and a half (700 mm, 28 inches) in length, and colored white, red and black.[6]

[/url]
Unicorn in [url=https://en.wikipedia.org/wiki/Apadana]Apadana, Shush, Iran

Ctesias got his information while living in Persia. Unicorns on a relief sculpture have been found at the ancient Persian capital of Persepolis in Iran.[7] Aristotle must be following Ctesias when he mentions two one-horned animals, the oryx (a kind of antelope) and the so-called "Indian ass".[8][9] Strabo says that in the Caucasus there were one-horned horses with stag-like heads.[10] Pliny the Elder mentions the oryx and an Indian ox(perhaps a rhinoceros) as one-horned beasts, as well as "a very fierce animal called the monoceros which has the head of the stag, the feet of the elephant, and the tail of the boar, while the rest of the body is like that of the horse; it makes a deep lowing noise, and has a single black horn, which projects from the middle of its forehead, two cubits [900 mm, 35 inches] in length."[11] In On the Nature of Animals (Περὶ Ζῴων Ἰδιότητος, De natura animalium), Aelian, quoting Ctesias, adds that India produces also a one-horned horse (iii. 41; iv. 52),[12][13] and says (xvi. 20)[14] that the monoceros (Greek: μονόκερως) was sometimes called cartazonos (Greek: καρτάζωνος), which may be a form of the Arabic karkadann, meaning "rhinoceros".
Cosmas Indicopleustes, a merchant of Alexandria who lived in the 6th century, made a voyage to India and subsequently wrote works on cosmography. He gives a description of a unicorn based on four brass figures in the palace of the King of Ethiopia. He states, from report, that "it is impossible to take this ferocious beast alive; and that all its strength lies in its horn. When it finds itself pursued and in danger of capture, it throws itself from a precipice, and turns so aptly in falling, that it receives all the shock upon the horn, and so escapes safe and sound".[15][16]
A one-horned animal (which may be just a bull in profile) is found on some seals from the Indus Valley Civilisation.[17] Seals with such a design are thought to be a mark of high social rank.[18]

https://en.wikipedia.org/wiki/Unicorn

Since your rejection of unicorns on those grounds was shown to be in error..wouldn't that categorically rule them out as "good reasons"? If, otoh, you insist that they remain good reasons, would being found in books full of myths and legends alongside clearly fictional creatures like dragons and sea serpents also be a "good reason" to reject gods?