Throughout the 7 books we are introduced to animals that exist only in the wizarding world. Why would the Ministry go to all the trouble of hiding them from muggles when lots of them are similar to animals that muggles are very familiar with? It seems like a waste of time and resources. What makes these animals worth hiding?
If you want more background on why magical creatures are hidden from Muggle eyes, then I recommend reading the introduction of Fantastic Beasts and Where to Find Them. It contains a “brief” history of Muggle interactions with magical creatures, and why, in 1692, the wizarding community decided to conceal twenty-seven species of creature from Muggle eyes.
A couple of reasons:
It could be dangerous for the magical community.
Dumbledore explains that Muggle sightings of magical creatures made the magical community less safe:
Imperfect understanding is often more dangerous than ignorance, and the Muggles’ fear of magic was undoubtedly increased by their dread of what might be lurking in their herb gardens. Muggle persecution of wizards at the time was reaching a pitch hitherto unknown and sightings of such beasts as dragons and Hippogriffs were contributing to Muggle hysteria.
(This follows a Muggle monk’s account of a particularly dangerous ferret, which Dumbledore guessed was a Jarvey, a sort of talking ferret.) That’s probably not as much of a problem today as it once was, but you can see why it was considered when the ban was first enforced. And the law has probably never been re-examined.
It would risk the secrecy of the magical community.
Today, we largely accept that creatures from historical legend are fictitious. Now imagine we found conclusive proof of dragons, and perhaps even proof that they’d existed for hundreds of years. That would cause us to examine a lot of assumptions about historical legends.
There are enough historical accounts of magic to make the magical community quite nervous. They don’t want us re-opening old wounds.
(If you read Fantastic Beasts, it sometimes explains what makes a creature unusual and worth hiding from Muggles. For example, Kneazles are “sufficiently unusual in appearance to attract Muggle interest”; remember that Crookshanks looks like a normal cat because he’s only half-Kneazle.)
This goes for small creatures too: enough sightings of weird-looking ginger cats is going to get prying eyes aroused.
It would be dangerous for Muggles and the creatures involved.
Muggles and unusual creatures don’t mix. There is a long history of humans hunting creatures to extinction, and even scientific missions of discovery can end with the creatures coming worse off. (For example, the giant tortoises that Darwin discovered on the Galápagos turned out to be so tasty that a lot of them got eaten.) Given Muggle barbarism, can the wizarding community be blamed for wanting to protect a few special creatures from us?
On the flipside, a lot of magical creatures would be dangerous to Muggles, who are ill-informed and ill-equipped to deal with them. (Remember that it’s a UK-centric universe, where guns among Muggles would be scarce.) There are lots of dangerous creatures – Lethifolds, Quintapeds, Dragons, Manticores – which would wreak havoc among Muggle communities.
First off, animals from the wizarding world would not react well to Muggles. A lot of them need special care and a Muggle wouldn't know what to do with it. The animals might be dangerous or exhibit magical powers.
Therefore (secondly), Muggles would be put in danger by being exposed to things like dragons and hippogriffs.
Thirdly, this would break the Statute of Secrecy, with was sanctioned for a good reason. The Wizards had some past experiences with Muggles and would not like to repeat that.