We know that double-colon (::) is used to get function (callable) reference in Kotlin, e.g. String::compareTo, \"string\"::compareTo.
In Kotlin you can write Object::class, which will give you a KClass. KClass is not equivalent to the class Class that we know from Java.
If you want to get the Java Class class you can write Object::class.java - i.e.:
println("string"::class.java)
Also in java, .class is not a method or a member - it is a special directive for the compiler to access the class.
I guess each language select the syntax that makes most sense for it, and kotlin's creators decided to use ::
:: in Kotlin is about meta-programming, including method references, property references and class literals.
See discussion about class literals.