It's that the idea of "bard=inspirational leader", Could be an Aragorn (?) could be a Conan (?). No.
Inspirational Leader/Supportive Guy is something any character should/could roleplay. In a game of D&D, for many people, I should not have/take a class to give/make me an "inspirational leader." That is something I get to decide if I want my character to be that or not. Characters of ANY class can be that...Be a fighter. Be a paladin. Be a barbarian...and ROLE-PLAY yourself as/in the "support", "scheming", "battle-hardened/knowledgeable", and/or "leading" role [as that word actually means, not the artificial jargon to justify design choices].
I think this is at the root of a LOT of the bard push-back. It's a class with no meaning/purpose that isn't/should not be achievable by any possible player roleplaying instead. I should be able to make an Assassin or Illusionist who is a bard. Forget about "if I multiclass xyz."
Ranger, nowadays/for those denying its roots in preference of the managerie it has become in the last 15 years or so, runs up against the same problem. A non-paladin "Knight" or Cavalier runs with this pack as well.
Be a fighter. Take outlander. Maybe a few levels of rogue thrown in and a sharpshooter feat [since everyone likes to talk and play as if these things are NOT optional]. There ya go. Ranger. Why do we need the class? Are you going to be Mr. Wilderness Warrior guy? Are you going to be "the druid's paladin"? Are you going to be Robin Hood or Aragorn? Are you going to wear the trappings and roleplay the kind of character you espouse?
Be a fighter. Take noble [or more exact/literal "noble variant: knight"]. Maybe a soldier for a more "down to earth" guy. There's your knight/cavalier. The rest is roleplaying. Are you going to be Ms. Honor/Chivalry/Code of Conduct? Are you going to wear the trappings and roleplay the ideals to which you espouse?
Be a fighter...or a cleric if you think it should be a heal-machine. Take noble or solider...or sage or folk hero, for that matter. Or be a warlord, fluff your non magic to not be magic if you like. Downplay or simply ignore your martial abilities. Throw on some healing spells. Some history skill. Maybe the inspirational leader feat. There's your bard. The rest is roleplaying.
Folks are objecting, I think without even knowing it in many cases, because the class is [or represents] a class that basically takes that roleplaying-part away from the player and bakes it [or a larger/large enough portion of it to ruffle feathers] into the class.
Roleplaying is NOT mechanics. It can not be replaced or overwritten by a list of class features. And that is something many people either a) don't understand, b) don't like/want to understand or c) don't care enough about to see the difference/problem. When you look at the bard...look at just about ANY of these threads about it...What is the "discussion" and grand majority of the disagreement [even among bard FANS!] about? The mechanics! What does the bard "get"? What does the bard "need" or its not a "bard"? What can they/should they/must they [a.k.a. "I should be able to"] do?