I don't refuse to use third-party libraries out of hand. If something is good, I'll use it. However, my assessment of the cost/benefit tradeoff differs from others. Take, for example, AFNetworking. It seems to be the gold standard for any iOS app that makes web calls, to the point where it's practically a default first step when making a new project for many programmers. Me, I don't understand the appeal. The cost is enormous due to adding a huge quantity of code (and therefore bugs) to your app, and the benefit over using what Apple provides is tiny.
If the cost/benefit tradeoff appears worthwhile, taking into account the large cost from adding any third-party code, I'm happy to make it. It just doesn't happen very often.
To me, CocoaPods doesn't move the needle on the cost/benefit tradeoff, because the cost of what CocoaPods handles is extremely small compared to the total. Thus why I don't really understand the point of it. It takes something that's infrequent and already easy, and makes it a little easier.