Why is fundamental physics taught in terms of particles? According to this paper, there can be no relativistic quantum theory of localizeable particles ("relativity plus quantum mechanics exclusively requires a field ontology"). Sean Caroll has also argued that fundamental physics should be conceptualized in terms of fields, not particles. Here is another paper on the subject as well, and two other related questions on this website.
My question is primarily about learning and conceptualization: Quantum fields, not particles, are the fundamental constituents of nature (at least as far as we know), yet particles are often the conceptual tool used to teach field theory/particle physics. What concepts do particles help explain where fields fail? And conversely, where do fields succeed while particles fail? 
Relevant article: Pitfalls in the teaching of elementary particle physics.

Elementary particle physics is gradually implemented into science
  curricula at the high school level. However, common presentations on
  educational, semi-technical or popular level contain or support severe
  misconceptions. We discuss in particular the notion of 'particle', the
  interaction between them and the use of Feynman diagrams. In many
  cases the true novelty of particle physics (i.e. quantum field theory)
  is largely ignored. We also suggest reasons for this widespread
  distortions of particle physics in popular accounts.

 A: 
A particle interpretation of QFT answers most intuitively what happens in particle scattering experiments and why we seem to detect particle trajectories. Moreover, it would explain most naturally why particle talk appears almost unavoidable. [My italics: the answer to your question.]

http://plato.stanford.edu/entries/quantum-field-theory/#TakSto
The reference discusses that the particle interpretation has serious problems indeed, and that the field interpretation also has problems!

The occurrence of unitarily inequivalent representations (UIRs), which first seemed to cause problems specifically for the particle interpretation but which appears to carry over to the field interpretation, may well be a severe obstacle for any ontological interpretation of QFT.

Two other ontologies are mentioned as possible candidates: Ontic Structural Realism (OSR) and Dispositional Trope Ontology (DTO).

In conclusion one has to recall that one reason why the ontological interpretation of QFT is so difficult is the fact that it is exceptionally unclear which parts of the formalism should be taken to represent anything physical in the first place. And it looks as if that problem will persist for quite some time.


I hope that this answer is at least useful in suggesting that the field interpretation isn't a "done deal", as suggested by the question. This answer merely suggests that particle talk may be just as good as field talk (namely: they could very well both be "wrong" for QFT, and, apparently, for similar reasons, ontologically).
A: Simply because it is usually taught from historical, heuristic and pragmatic point of view, rarely from axiomatic point of view (e.g. Wightman axioms, as mentioned in a comment by ACuriousMind).
This is because it is taught to be useful, as most QFT calculations boil down to scattering and decay amplitudes, and as Sean Carroll said:

Heuristic QFT, on the other hand, is what the vast majority of working field theorists actually do — putting aside delicate questions of whether series converge and integrals are well defined, and instead leaping forward and attempting to match predictions to the data.

A: From a decoherence point of view, fields are more fundamental as they give rise to particle-like behavior from the wave behavior if interactions with the environment are strong. In the end though, quantum mechanics only describes correlations between macroscopic changes in detectors (or other materials), so whatever kind of ontology you want to take in the microscopic world is more a matter of preference.
Some more speculation of my own (might be controversial to some):
It is important to note that quantum mechanics does not describe single events, while we do observe these events. In this sense, it seems difficult for me to think of fields or wavefunctions as fundamental, since they do not describe any single situation and only ensembles. Another way to put it, according to the view of Bohr, is that in order to arrive at quantum mechanics we have to presume that we observe these single definite events which occur in our classical-like realm.
A: There is a particle ontology of QFT. The Path Integral formulation is a particle ontology i.e. particles are the things that "exist". 
The Wikipedia article says: 

The path-integral approach has been proved to be equivalent to the other formalisms of quantum mechanics and quantum field theory. Thus, by deriving either approach from the other, problems associated with one or the other approach (as exemplified by Lorentz covariance or unitarity) go away.

with a reference to Weinberg's Quantum Theory of Fields textbook, chapter 9. 
So to answer your question: "Why is fundamental physics taught in terms of particles?" 
Because it is fundamentally correct to teach QFT in terms of particles using the way it is taught(Path Integrals), and the teaching curriculum also includes proof that this approach is correct.
If someone claims "particles are wrong" they either assume particles to have extra properties e.g. definite position, volume, so that they can refute their own idea of a particle, or they just say that they philosophically prefer to imagine fields, because the particle intuition does not work, but in QM none of the usual intuitions work, so that is not a very strong argument.
