Calling the plurality of political conflict from 45 to 90, and like several fields of study, semantics is kinda crazy work but you’ve got the spirit in general I guess. Good day as well.

on the left side of the political divide

There is no such political divide, at the minimum there are a couple of axis on which to place peoples and groups political position. There can be such a thing as three or more fundamentally opposed political positions(liberal, left, fascist, monarchist,…) and there can be a united opposition of two or more of these opposed to another. As would from some point of view ideally be the case with left and liberal politics being united against fascist politics. This does not make left and liberal politics the same or part of the same thing. They are fundamentally opposed in a way where the underlying assumption of the philosophy that defines them are incompatible so that accepting one of these assumptions makes accepting the other impossible.

refusal to unite against fascism

it’s not productive as you said but I think there can be much said about the concept of accepting that one can fight fascism without outwardly doing it towing a liberal party line. Said another way if liberals will not join leftists in their way of fighting fascism, why should the reverse be generally true.

In all honesty it just feels like a case of US brained political understanding or just like not well read. It’s the kinda environment where someone will call out Mamdani, sanders, obama, and bill gates for not uniting under one flag to fight orange hitler. Maybe they will but it should be obvious that it’s gonna be a temporary and strenuous marriage at best.

From https://en.wikipedia.org/wiki/Left-wing_politics paragraph 3 and 4 it should illustrate why Obama is not considered part of the Left even though part of his campaign and probably governance could be considered center-left

Ideologies considered to be left-wing vary greatly depending on the placement along the political spectrum in a given time and place. At the end of the 18th century, upon the founding of the first liberal democracies, the term Left was used to describe liberalism in the United States and republicanism in France, supporting a lesser degree of hierarchical decision-making than the right-wing politics of the traditional conservatives and monarchists. In modern politics, the term Left typically applies to ideologies and movements to the left of classical liberalism, supporting some degree of democracy in the economic sphere.

Today, ideologies such as social liberalism and social democracy are considered to be centre-left, while the Left is typically reserved for movements more critical of capitalism ,[9] including the labour movement, socialism, anarchism, communism, Marxism, and syndicalism, each of which rose to prominence in the 19th and 20th centuries.[10] In addition, the term left-wing has also been applied to a broad range of culturally liberal and progressive social movements,[11] including the civil rights movement, feminist movement, LGBTQ rights movement, abortion-rights movements, multiculturalism, anti-war movement, and environmental movement,[12][13] as well as a wide range of political parties.[14][15][16]‌

The problem is more that people conflate liberal and left through Obama. Like you are doing in this very comment. If you know what left politics is it’s obvious that Obama isn’t part of this.

If Obama is good or bad, whether he carried some better than conservative policy, or got something done really doesn’t matter because he isn’t a left politician, so placing him as one will generate resistance not because everyone on the left sees him as evil, but because he is obviously not left to people who understand what ‘left’ and or ‘liberal’ means.

It’s an error in categorization on the part of the one conflating Obama and left, not a failure of “left purity” on Obamas part, he never was left to anyone paying attention, at best he used left messaging and heritage to promote a liberal campaign. Which might be the second reason many are sometimes angry with him, he used left aesthetics and talking points, while in retrospect not caring all that deeply about them, which to someone starting out naively optimistic about the prospect of an Obama White house, feels like betrayal, not because Obama really betrayed them as such, more because over time they came to realize he was never really fighting for them to begin with.