On what does Lutheranism base itself to say that it has the right interpretation of Scripture?
Well, I suppose Lutheran teachings are more "intellectual" in nature than "emotional".
I don't know much about many denominations, but I do know a bit about Baptists (half of my family is, and my fiancé used to be before she converted to Lutheranism).
I will use an example, hopefully in a successful attempt to illustrate my meaning of "intellectual" over "emotional".
One main difference I can think of is how one is saved. Baptists emphasize a person asking Jesus into their heart, and feeling that conversion experience. Lutherans, on the other hand, emphasize "saved by Grace, of God, not of ourselves." That is, God saves us by His grace. God provides it.
Scripture tells us we must trust Jesus as our Savior. This trust comes from teaching, and not an emotional rush (as some of my Baptist friends have described it). The problem I, as a Lutheran, find with the "emotional" side, where a person asks Jesus into their heart, etc., is that it is something like: When
I ask, when
I decide, when
I feel, that's when I'll be saved.
Is salvation something we do, or something we're given? If we're given salvation, then it is not up to us to ask for it. It is merely up to us to accept the Gift of Grace. But if we must seek it, if we must decide, usually as a result of an emotional rush, then it is of us.
Yet we are taught that we are saved by grace through faith, so no man may boast because of his own works.
In short, Baptists say we must ask Jesus into our heart, feel the conversion experience (something that happens naturally when one asks Him into one's heart). Lutherans say that we must trust Jesus, believe in him, but that comes from the Holy Spirit. It's a gift from God, one that we don't ask for, but one we receive in full gladness.
That's the best I can think of for explanation right this moment. I may have more for you later.