Why is string theory considered the best candidate for quantum gravity if it cannot resolve singularities? The reason we want a theory of quantum gravity is to be able to understand singularities like the big bang and black holes.
However the best candidate so far for such a theory, string theory, does not resolve those singularities, in fact it makes things worse introducing black branes.
My question is why do we consider string theory to be the best candidate for a quantum gravity theory if it cannot make any prediction that cannot be made by general relativity and quantum field theory like resolving singularities?
 A: 
The reason we want a theory of quantum gravity is to be able to understand singularities like the big bang and black holes.

I would say the reason we want a theory of quantum gravity is because, as good reductionists, we want to have a complete, unified description of reality. We know the Universe is quantum mechanical, and that gravitation exists, and therefore we know we need to unify these theories.
At that level, string theory is successful at providing a quantum mechanical framework that appears to be consistent, and contains gravity. In fact, even better, it also contains matter fields in the same framework, and it's conceivable that somewhere in the vast landscape of string theory vacuaa, is one that looks like ours.
Having said that -- yes, we do want to understand the black hole and big bang singularities, and quantum gravity is supposed to provide the tools for us to resolve them. While there are proposals like the fuzzball proposal for black holes, I think it's fair to say there is not a consensus for how the black hole singularities get resolved in string theory. And it's also not currently known how to handle string theory on time-dependent backgrounds, which we need for cosmology.
One attitude (which I'm not unsympathetic to) is to be hard-nosed and say, essentially, string theory has had decades of work put into it; if it can't be used to convincingly answer the basic physics questions we have about quantum gravity, what good is it?
On the other hand, string theory does provide a candidate quantum theory of gravity, which we need, and is still a work in progress. There's no promise that any particular question should only take a certain amount of time to answer, and the black-hole and big-bang singularities are deep questions very far from the regimes where we have experience with physics. While we lack the understanding to solve these problems now, maybe with more insight we can solve these problems. There has been work over the past few years in trying to understand the interior of the black hole using the AdS/CFT correspondence, leading to a possible solution to the black hole information loss paradox, so there is progress being made.
Having said all of that, I think a common, modern attitude toward string theory held by many (of course not all) string theorists, is that it is a useful set of tools for understanding physics, but it's not clear whether or not it is the theory of everything. Many string theorists now work in the area of applying AdS/CFT to other areas of physics outside of quantum gravity such as condensed matter physics; for example, see https://arxiv.org/abs/0903.3246.
A: *

*String theory does have a theoretical resolution for the singularity problem - the fuzzball.

*String theory is not the only game in town - loop quantum gravity is still a viable candidate.

