Why would the Founders of Hogwarts have needed to hide from Muggles?

Question

"You all know, of course, that Hogwarts was founded over a thousand years ago – the precise date is uncertain – by the four greatest witches and wizards of the age. The four school houses are named after them: Godric Gryffindor, Helga Hufflepuff, Rowena Ravenclaw and Salazar Slytherin. They built this castle together, far from prying Muggle eyes, for it was an age when magic was feared by common people, and witches and wizards suffered much persecution." Harry Potter and the Chamber of Secrets, chapter 9

So apparently Hogwarts was hidden in order to protect the Witches and Wizards from the Muggles of that age. Given how powerful the Founders (and, it is implied, all magic was) back then, why would they have needed to hide?

Answer 1

Muggles were afraid of and far outnumbered wizards, and Hogwarts had untrained ones.

As your own quote says, Hogwarts was founded when a fear of magic was common.

They built this castle together, far from prying Muggle eyes, for it was an age when magic was feared by common people, and witches and wizards suffered much persecution." - Harry Potter and the Chamber of Secrets, Chapter 9 (The Writing on the Wall)

The Founders had to hide Hogwarts because many Muggles feared magic. Muggles far outnumbered wizards, so if Muggles decided to destroy Hogwarts, they'd likely either succeed outright or else do a lot of damage, even if wizards are more skilled generally. Mobs and guerrilla tactics can eventually defeat even the most skilled opponents, especially if their numbers are small. We know there are far more Muggles than wizards, so the Muggles would either win or decimate the wizarding population in a Muggle/wizard war.

In addition, while the faculty might have a better chance of defending themselves, the majority of Hogwarts would be young wizards being taught to use magic, so they'd be relatively defenseless. Hogwarts would be an easy target for Muggles trying to lessen the number of wizards. If the Muggles knew of a place where they were training young wizards to do magic, of course it would be an obvious target. Not only is it somewhere that only wizards would gather, but most of them would be untrained students and therefore easier to kill.

Answer 2

Wizard-Muggle relations were pretty bad back then. This lead to several possible reasons for hiding:

• Hogwarts was meant to be a school, not a military fortress, and fighting off Muggles would have interfered with the education. Hogwarts would either be less effective or require more wizards for protection against Muggles.
• Open conflicts, like around a castle, would have worsened the relations between wizards and Muggles. Why risk that, if hiding seems to be possible without any problems?
• There was an enormous risk to wizardkind, should Hogwarts be succesfully attacked by muggles. Seven years of wizard breeding could be wiped out in one unlucky instance. Additionally, the damage to the school's reputation could be fatal.

With all these points in mind, what's the point in not hiding?

Even if the wizards somehow desired a conflict with ignorant Muggles, they could choose any place for it. Why the school? Normally, people tend to make sure their children are safe.