Clinton has claimed that it is an insult to refer to anyone as being part of the "political establishment" -- and that Sanders is "establishment", not her! In the context of comparing Democratic candidates and institutions during the Democratic primary, it should be obvious that we are talking about the Democratic Party establishment. How could it be an insult to point out who is and isn't part of that?
Clinton has the overwhelming majority of endorsements by Democratic Party officials, as well as endorsements from the leaders of unions and other organizations closely aligned to the Democratic Party. Sanders has been endorsed by a few fringe Democratic officials and by some Democratic-aligned organizations that polled their membership. Clinton has made this disparity one of her key selling points, correctly noting that these relationships within the party structure give her power to get things done within the party.
So it's seriously disingenuous to claim that it's an insult to point out that Clinton, along with Democratic Party officials and those running some Democratic organizations, are part Democratic Party establishment that she brags about being connected to. And after months of attacking Sanders by (correctly) noting that his political career has been apart from the Democratic Party establishment, it's bizarre for Clinton to have argued that he's "establishment" and she isn't.
If you want to work within the existing Democratic Party establishment, then Clinton's credentials as an insider are a good reason to support her. If you think that the Democratic Party establishment needs to be fundamentally changed, then Sanders' credentials as an outsider are a good reason to support him.
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There’s a better way to handle this sort of thing. If someone calls Sanders a communist, he'll reject that as an insulting lie. But when someone calls him a socialist, his reply is "damned straight I'm a democratic socialist -- this is what that means, here are the policies and goals I'll fight for, and if you like them, please help me fight for those goals.” He doesn’t say “you are insulting me — and you are the real socialist.”
Pointing out insider/outsider status in the Democratic Party establishment isn't an insult to either of them or to anyone else. It's just correctly noting one of the contrasts between these two candidates. We each have a right to decide which status we prefer, but not a right to deny obvious facts about who has which status. Especially not when a candidate brags about their status.