Okay some background - I am a Theoretical physics graduate student (and i would go even further calling myself a math person) and quite recently I have been into this question and am finding it hard to justify to myself as to why I choose it. And I "was" a member of one of those elite sects who declared that theoretical physics is the fundamental truth/science of nature.
So one day, I was the sole astrophysics grad student and in a CMT seminar, when the professor talked about making a model "x" for a system (if you want to know, it is for graphene) with which he initially started worked with the action and did stuff to it to later realize that it dint fit the experiment "y". so he had to modify his model from "x" to "x1" by bringing in new ideas to make it fit "y". So I asked him what would you do with this model "x1" ? He said this could predict the result of another set of values for exp "y1".
So after thinking about it the final thoughts - 1) Theoretical people are model builders in different scale be it Cosmology or biophysics or CMT only at different scales and using different tools.
2) Once these models are built, we are solely motivated to change our model until it fits the existing experimental data, and keep on modifying the model if it still does not fit future data. (expect for phenomenology where you do not have sufficient data eg.. Massive gravity, SUSY, String etc..)
Can someone explain to me the uses of these models if they cannot guarantee the results of a new experiments (I know this is impossible to do, like to build a theory that will for sure predict future exp results), but if you cant, what is the point of building just theories ?
PS : Now I have moved myself from the theoretical sect to accept the fact that exp is more fundamental than theory. (I guess someone answer here could change my mind?) Since I came to physics for the mathematical rigor I needed to understand stuff, I don't think exp caters to it. So I have decided to move to computational part of physics where again one makes model, but are not limited just by analytically solvable models and is inbetween exp and theoretical.
PPS : This question is not to condescend on theoretical physicists ( I am one) or experementilists (now a strong believer of exps!) but rather to reason out as to why I choose this field. It seems like everyone had big ideas about how physics works when in high school and one they reach the level of field theory and other hardcore subjects, get trapped in solving problems missing the big picture. I initially thought I choose theoritical physics (I was an engineer by undergrad and hated the lack of details and the fact that every other formula is empirical) because of the rigors structured mathematical convincing I wanted to understand things, but then latter realized if that's what I seek for, then I should have taken pure abstract math. Then came across this awesome book "feynmann's rainbow" by Mlodinow, where he talks about two kind of rigors that physicist have - "mathematical rigor" and "logical rigor" and I am now convincing myself that having a logically rigors proof is as acceptable as a mathematically rigors proof. While self searching as to switch to pure math or to continue on physics, I found myself trapped in this question.