It is primarily by raising interest rates that central bankers curb inflation, but an increase in interest rates takes up to two years to affect inflation.
Conclusion (thus)
Central bankers' success in temporarily restraining inflation may make it harder for them to ward off future inflation without incurring the public's wrath.
Evidence
The main tool central bankers have for curbing inflation is raising interest rates, but it can take up to two years for an increase in interest rate to affect inflation. Thus, central bankers need to kind of "guess early" and raise rates before inflation is excessive (possibly before inflation is even apparent).
But when people don't see clear evidence of inflation and interest rates go up, the public will feel like the central bankers are needlessly restraining a growing economy.
Evaluate
This argument is kind of like when your parent told you to pee before you left on a long car trip. You don't have to pee yet, so you're like, "C'mon, Mom, stop nagging me to pee." But in order to avert a bad situation later, you need to pee now.
Similarly, in order to avert a bad situation later (inflation), central bankers have to take an early action of raising interest rates. Since the public doesn't see an imminent need for raising interest rates, they end up getting mad at the central bankers.
The question is asking us about the very first claim in the paragraph. It's certainly part of the author's Support. It helps us to understand the precarious situation the central bankers are in.
They are tasked with helping an economy to avoid inflation, and their primary (i.e. #1) tool for doing so is a device that takes a while to make a difference (like turning the rudder of an aircraft carrier).
Goal
Look for something saying this first claim is a premise that helps us understand why central bankers need to act early enough that it confuses normal people who don't understand why these bankers are taking action so early.