I don't know why that "word choice" is controversial. The FBI is not in the business of "prosecuting" crimes in the legal sense, they are an investigatory body, it's in the name. The FBI absolutely CAN investigate egregiously, for example by falsifying evidence, or eliding exculpatory evidence, which they have a long history of doing.
The mere existence of an FBI investigation can seriously injure the affected party, and so in that regard the FBI has tremendous power to influence people and organizations, and is an obvious organization to co-op if one wanted to wield political influence nefariously. The natural stance towards the FBI should be one of skepticism and apprehension at a minimum, if not outright deep suspicion.
I think what many people are pointing out is that left-wing politicians openly supporting the FBI, CIA and NSA in any capacity is a blatant about-face, and just downright distasteful, particularly when the most high profile "investigations" of late are political in nature.
Edit:
A simpler way of expressing this would be to point out that the FBI serves the same function as the "State Security Service(s)" of countries that we don't like.