So I saw this passage:
Save me from the lion's mouth: for thou hast heard me from the horns of the unicorns. [Psalms 22:21]
And that was weird so I looked up all mentions of them in the Bible and I found a lot like these:
His glory is like the firstling of his bullock, and his horns are like the horns of unicorns [Deut 33:17]
And the unicorns shall come down with them, and the bullocks with the bulls; and their land shall be soaked with blood, and their dust made fat with fatness. [Isiah 34:7]
God brought him forth out of Egypt; he hath as it were the strength of an unicorn: he shall eat up the nations his enemies, and shall break their bones, and pierce them through with his arrows. [Numbers 24:8]
Will the unicorn be willing to serve thee, or abide by thy crib? Canst thou bind the unicorn with his band in the furrow? or will he harrow the valleys after thee? [Job 39:9, 10]
I'm not even sure when unicorns first appeared in myths but why are they in the KJV?
Well, the sad news is that they are not unicorns as you (probably) imagine them.
Underlying all these verses is the Latin Vulgate's unicornis which sounds like what it is "one-horn", reflecting the Greek LXX μονόκερως, also "one-horn", and then the Hebrew רְאֵם but the Hebrew is now usually translted as (wild) ox, not unicorns.
The Hebrew term basically refers to a some kind of powerful, horned beast. A large wild ox is indeed possible, but we're not entirely sure (animal and plant terms can be particularly difficult to pin down). Some take it to be a reference to the aurochs, or to a rhinoceros.
Interestingly Dt 33:17 in the Latin has rhinoceros rather than unicornis.
So, even though the the KJV represented a translation that returned to the Hebrew for the Old Testament, scholarship on Hebrew language at the time was still largely influenced and mediated by the LXX and Vulgate, and 'unicorn' was the term chosen. Partly because 'unicorn' is rather vague too - we think of a mythological horse with a single horn, but it's not clear that a an early 17th century English speaker would. Indeed, if you compare descriptions of Pliny (1st century) and Isidore of Seville (6-7 cent. CE), the 'mental' picture that an original reader of the KJV would have had is much closer to rhinoceros than to 'horned horse'.
To give a direct answer, it's not that the re'em is evil, per se, but they are threatening, because they are big and powerful wild animals.