Let's take a look.
Let's start with some background:
16 So Jesus answered them, “My teaching is not mine, but his who sent me.Now, look back at the very first verse.
17 If anyone's will is to do God's will, he will know whether the teaching is from God or whether I am speaking on my own authority.
18 The one who speaks on his own authority seeks his own glory; but the one who seeks the glory of him who sent him is true, and in him there is no falsehood.
19 Has not Moses given you the law? Yet none of you keeps the law. Why do you seek to kill me?”
20 The crowd answered, “You have a demon! Who is seeking to kill you?” 21 Jesus answered them, “I did one work, and you all marvel at it.
22 Moses gave you circumcision (not that it is from Moses, but from the fathers), and you circumcise a man on the Sabbath.
23 If on the Sabbath a man receives circumcision, so that the law of Moses may not be broken, are you angry with me because on the Sabbath I made a man's whole body well?
24 Do not judge by appearances, but judge with right judgment.” (John 7:16-24, ESV)
There's the answer. Christ's teachings weren't His own – at least not the human aspect of Himself. Rather, they were teachings from God.
Paul tells us as much when he selects various Old Testament Scriptures to say, 'None is righteous, no, not one.' James warns that if we break one commandment, we might as well have broken them all. When you look at the Commandments, you can pretty easily see there's no way anyone can make it through a day (even less) without breaking at least one of them.
So, right (or righteous, as in the KJV) judgement can't possibly our own judgment – our judgement is flawed because of our sinfulness. Our own judgment is filled far too often and far too much by our own thoughts, feelings, and opinions; we need an objective standard by which to judge rightly and righteously.
That'd be God's standard.
And we're in luck. In His infinite wisdom, He's made His standards clear to us in a collection of writings we now call the Bible. We don't know everything about Him, but we know enough to know what He expects from us. We know right from wrong, good from evil, precisely because God tells us in His Word – the Bible.
Can we judge rightly and righteously? Apparently so, since Christ told His adversaries to do so. We just need to know which standard to apply when we judge.
And God's made that pretty plain to us.
Unless, of course, we don't read His book.