Explaining that without coming across as a "troublemaker" can be pretty difficult. You just sound like you're ragging on the company / people rather than explaining the issues well. And do you really want to get in a deep conversation about cultural issues at your previous company?
“the software development manager was originally hired to bring new thinking into a company in $small_town so he spearheaded opening an office in $bigger_city. After awhile, the old guard pushed him and my manager out and that left us without a voice in the satellite office and our input was ignored. I want to be somewhere which allows me to be impactful”.
It would have been a lot harder to explain if I actively didn’t get along with my managers.
And yes, as the hiring manager, I may want to understand the cultural issues at your last company. Why?
Because I want to understand (a) what you value, (b) how you deal with conflict, (c) will you be able to help me improve our culture here and (d) what cultural issues you may or may not bring with you.
If I'm going to help you be successful here, I do want to understand your background. I may not need all that information before hiring, but I will get to it eventually because it's pertinent to helping you and the team succeed.
Sometimes a person sees bad shit and just runs, and that's a valid approach. Psychoanalyzing every decision they make is the trap of interviewing.
“How can I moderate this conversation so the questions themselves are not obstructing the candidate’s answers?”