From Quantum Mechanics to Quantum field theory to String theory? Today during a very "unique" study session, I might have internalized why  Quantum mechanics was not enough, and Quantum field theory makes sense.  It seems the reasons are that 


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*When a potential is used in Quantum mechanics, we explicitly violate special relativity because information would have to travel faster than light

*In QFT particle creation and annihilation are understood nicely as natural implications of what can happen if the kinetic energy of the combining species  is larger than the rest mass of some created pair

*Space and time are not on an "equal footing" in QM

*Decay processes are a testy issue
These things are starting to mean something to me. What is the reason for string theory, what does it make natural and clear that QFT falls short of?
 A: One has to keep clearly in mind the structure of present day physics.
Quantum mechanics is the theory that started as non relativistic with the Schrodinger equation for potentials, and became relativistic with the Dirac and Klein Gordon and quantized Maxwwell equations. Quantum mechanics has postulates which used with the solutions of the differential equations describe single particle potential problems correctly and it has been validated beginning with the hydrogen atom etc.
Quantum field theory is based on the solutions of the above equations and has been developed to describe quantum mechanical interactions which are a many body problem, as can be seen in any Feynman diagram. Quantum field theory is founded on the free particle solutions of the above QM equations and obeys the postulates of quantum mechanics.  The creation and annihilation operators act on the appropriate ground wave function of the problem at hand.
The success of the SU(3)xSU(2)xU(1) model of particle physics which has unified the three interactions , strong, weak, electromagnetic, lead to the holy grail of unifying gravitational interactions to the other three. That is what lead to string theory models becoming important. Quantization of gravity exists only as effective field theories, because no renormalization program can remove the singularities inherent in the spin two higher order exchanges of gravitons. It has been shown that string theory has a group structure that can accomodate the standard model and also a representation of a spin two particle that can be assigned to the graviton; with supesymmetric models calculations of higher orders give finite results which is the reason there is such an effort in string theory research. The problem is no definitive model has been found among the thousands of possible ones, up to now.
A: As you said in your question, quantum field theory is very important; it takes the ideas of quantum mechanics and applies them to fields, such as the electromagnetic force (in fact, quantum electrodynamics was the beginning of quantum field theory). Quantum field theory has plenty of evidence to support it, and it is still an ongoing work. String theory, though, is very different. In reality, string theory has very little evidence to support it. Right now, it's basically an idea, and what supports it are the dualities embodied in m-theory. Now, for string theory's advantages:


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*Some scientists believe its use of the anthropic principle is an advantage (to explain this in a nutshell, the string theory predicts so many universes some scientists believe this explains away the fine-tuning of, for instance, the cosmological constant, though there is more to the anthropic principle and this issue than that). 

*It provides  a framework for combining particle physics and general relativity.

*Currently, the model of physics we use is called the standard model. While this model is incredibly useful, there are some things it cannot do - for example, it fails to incorporate gravity. Scientists hope string theory might create a path toward combining quantum theory and gravity. 

*The Big Bang doesn't fully explain everything about the beginnings of the universe and cosmic inflation is the theory believed to be our best shot at moving forward. Cosmic inflation needs a particle called the inflaton, whose properties can't be derived from cosmic inflation but might be able to be derived from string theory.


However, it must be kept in mind while reading this is that string theory isn't on nearly as strong of a footing as quantum field theory. There are many kinks to be worked out, and there isn't really any evidence for it. I hope this helps!
Here's Wikipedia's article on string theory, which goes more in-depth into some of this and also explains some of string theory's problems and mathematics:
https://en.wikipedia.org/wiki/String_theory
