Many people don't realize that there is a world of difference between trying to prove theology with scripture and proving theology from scripture. What do I mean by these two terms? Let's take a moment to examine them.
From scripture refers to teaching theology directly from the pages of scripture and from relevant verses. That is, teaching justification from justification verses, teaching about works from passages about works, teaching about the deity of Christ where that is clearly the topic or part of what is being discussed, etc. For example, John 14:6 is, from the immediate context and the context shown around it, is obviously a passage about salvation and the Solus Christus nature thereof, and so it can be used for those related topics.
With scripture refers to teaching theology using scripture, but in a roundabout way. That is, you attempt to use a passage of scripture as maybe an "example" of what you're talking about, or you're using a passage of scripture to teach something that the passage clearly isn't teaching about. Countless examples of this were seen in Rob Bell's book Love Wins (see my review of it here): the Parable of the Rich Man and Lazarus was used to teach about Christ's resurrection (which it wasn't about, at all); the Parable of the Prodigal Son was used to teach about heaven and hell (which, again, it wasn't about, at all). They were tied only loosely to the topic, so that the undiscerning might have been unable to understand how Rob Bell had used them grossly out of context.
Being able to discern between these two is vitally important in our treatment of scripture, and for a two-fold reason: 1) it helps us to understand the topic being discussed in the larger context; 2) it presents us with a stronger root in the teachings of scripture, certainly much stronger than a string of weak proof texts.