This is a tricky one, but the basic issue involves the distinction between a sufficient assumption and a necessary assumption. Even if exercising the muscles on opposite sides equally doesn’t guarantee a healthy back (essentially, (C) negated), that doesn’t mean that it’s not important. Maybe you have to exercise them equally AND take a vitamin pill (in other words, it’s possible that there is another necessary condition, besides the exercise). Now, (C) is not true – balanced exercise doesn’t guarantee the healthy back, because you still need to take the pill. But the argument isn’t hurt, because exercise is still important – if you don’t do the balanced exercise, then you’re not going to get the healthy back. You have to do both – the exercise AND the pill.
Let me give you an analogous argument – to become a lawyer, you have to pass the bar, and you also have to pass a background check. Therefore, in order to become a lawyer, it’s important to pass the bar. In my analogous example, (C) basically says, if you pass the bar, you’re guaranteed to become a lawyer. Let’s negate it: If you pass the bar, you still might not become a lawyer. The reason that doesn’t hurt my conclusion that it’s important to pass the bar is because if you don’t pass the bar, you have no chance of becoming a lawyer. Satisfying the necessary condition is still important, even though it doesn’t guarantee success.
The conclusion of the passage is that it’s important to exercise the muscles on opposite sides equally; the right answer, if negated, should lead us to believe that it’s NOT important to exercise them equally (or at least that the notion that it IS important is not supported by the passage). Look what happens when you negate (B), in contrast to (C): If (B) is negated, then exercising the muscles unequally doesn’t lead to unbalanced muscle development. If that’s the case, then the argument falls apart – it’s not important to exercising them equally if you can exercise them unequally without getting unbalanced muscle development.
In more general terms, the argument is written such that the balanced exercise is necessary. That’s what (B) gives us. The argument doesn’t need the balanced exercise to be sufficient. That’s (C).
Please fell free to follow up here or send a private message if you could use clarification; this is a tricky one.