The absolute laziest sentence in any Bible discussion is "that's just your interpretation". It shows no effort what so ever, and can be used against literally any interpretation, no matter how reasonable, and ironically, even against the positions of the one saying it. Sure, my position is "just my interpretation", but your position is just yours. If, indeed, it is yours, as this saying also comes from people who, rather than interpreting the Bible, will interpret someone else's interpretation.
In reality, while there may even be a handful of interpretations of a given scripture, they are not all equal, nor are they all even valid. To illustrate this, I like to cite Isaiah 43:10: "Ye are my witnesses, saith the Lord, and my servant whom I have chosen: that ye may know and believe me, and understand that I am he: before me there was no God formed, neither shall there be after me." Christianity is a notoriously monotheistic faith. We believe in one God, we worship one God, we don't believe in other gods, we don't believe we will ever become gods. Mormons do.
Of course, when I speak to Mormons, I have to switch examples. I can't very well cite Mormon beliefs as examples of invalid Biblical interpretations when speaking with a Mormon. A Mormon will look at that, see me teaching Monotheism, and say "well, that's just your interpretation". But for everyone else, Isaiah 43:10 is conclusive proof of Monotheism. There is... one God. The Mormon belief that "as man is, God once was, as God is, man may become" is objectively wrong, and not even the "authority" of their Church can change that.
But it's not even just denominations; individuals are quite fond of just drawing their own conclusions, too. Look at the hoops modern Liberals jump through to justify Evolution, abortion, homosexuality, all sorts of weird and worldly stuff. Show where the Bible says that's wrong, suddenly "that's just your interpretation".
But the great thing about the Bible is it isn't as open to interpretation as the clouds, or an ink blot test. It is a rather large collection of meaningful words. Words which, according to scripture itself, make us wise for salvation, are useful for doctrine, reproof, correction, and instruction in righteousness, and do all this so the man of God may be complete and thoroughly equipped for every good work.
"But that's just your interpretation". Yes. How do you know it's my interpretation? Because you're reading me the same way you should be reading your Bible. There are thoughts in my head, I want to put them in your head, how do I do that? By writing them down in our common language. So how does God give us His thoughts? Through the Bible, which is not as open to interpretation as most people claim. It has a meaning, and that meaning can be understood by anyone capable of reading it. And if you can't read? Someone can read it for you, and you can still know what it says.
So you see just how lazy this kind of response is. But it is also rather telling. See, while some interpretations are better than others, "that's just your interpretation" is usually said by those with the bad interpretations. People who don't care what the Bible actually says, they just want it to agree with them. People who don't actually read the Bible, they just know a verse or two. People who cite only a few verses, if indeed they dare to finish the verse. People who practice eisegesis rather than exegesis. Basically, people who want to be their own God. But what you will notice is that they will never make more than a flimsy attempt to show why "your" interpretation is wrong, or theirs is better.
Of course, the reason for this is that it never actually is. They can't explain the flaws in "your" interpretation because if there are any, they don't know the scriptures well enough to correct you. They can't show why theirs is better because it isn't, it's something they, or someone else they are influenced by, have come up with for their own purposes.
"That's just your interpretation", therefore, is one of the laziest, and weakest, of all statements one can make in a discussion. Anyone who makes it, and doesn't immediately follow it up with either "here's why it doesn't work", or "here's why mine is better", should be considered unqualified, for reasons of either ignorance or malice, to discuss the given topic. They are incapable of defending their views, they are incapable of attacking yours, and the chances are extremely high that the reason for this is they know they're wrong, and don't care.