I think you're injecting your personal views into the definition, which don't align with the common meaning of the word.
Here's the definition of the word taken from macOS's built-in dictionary (New Oxford American Dictionary):
> leftist, noun: a person who has left-wing political views or supports left-wing policies.
> left-wing, noun: the section of a political party or system that advocates for greater social and economic equality, and typically favors socially liberal ideas; the liberal or progressive group or section
Anti-capitalist thought represents a subset, but is certainly not the sole marker of left-wing political thought.
Now, my _personal_ take on this is that western left-wing thinking and liberalism (in the moral philosophical sense) are deeply intertwined (given the Enlightenment and its values), but anti-capitalist thought is deeply illiberal in nature. It is this fundamental contradiction that leads to permanent infighting within the left-wing spectrum.
> I think you're injecting your personal views into the definition,
I think I'm injecting what I know from getting a degree in political science and a two and half subsequent decades of experience paying attention to how political terminology is used by scholarly, journalistic, popular, and activist sources across the political spectrum into the definition.
> Here's the definition of the word taken from macOS's built-in dictionary
And that's a tolerably decent definition for a relatively compact general dictionary, but it misses a lot of nuance; outside of activist sources using it as a slur for their opponents, it is not used in nearly the local-politics-relevant way that left/right (especially qualified with a national label, like "American left") is.