Socialism alone can’t solve social problems because society is much more than the division of labour. All social problems seem to be like the problem of labour, but solving the problem of labour doesn’t mean that the other problems will be solved simply by association. In contrast, anarchism addresses all problems at all levels simultaneously. Thus the Left can be part of anarchism, but anarchism is broader than the Left.
This reasoning can be applied to veganism, anti-statism, anti-fascism, anti-racism, anti-imperialism, indigenous rights and so on and so forth. These and others are potential allies of anarchism and also part of anarchism, but to make this clear let’s take patriarchy as an example by comparison to capitalism. Capitalism was initiated by the capitalists, not the workers, and this division has persisted. The propaganda and the law enforcement really only offer one solution to the workers; to become capitalists themselves and thereby reaffirm the system.
Similarly, it is men who have benefitted the most from owning their wives through the institution of marriage. The propaganda and the law enforcement again only offer one solution to e.g. non-male and non-straight people: striving for equality in the form of an equal share in the ownership in a formal marriage, which thereby reinforces the system.
Obviously, the ultimate solution in both cases must be to tear down these structures rather than attempt to push one individual up the ladder at a time, even though it pains us to see all the people on the bottom. However, if we can’t figure out how to solve the structural problems, we are forced to fight for equality within the system until we figure it out.
P.S. Previously I have described anarchism as part of socialism and historically there is some truth to that, in particular regarding the fact that anarchists were part of the First International and then got kicked out. However, there were anarchists already before then. (There were also socialists before Marx(ists) claimed a monopoly on the words socialism, communism, leftism, workerism which makes the problem even more complicated.)
P.P.S. Compare it to anarcho-capitalists. They define anarchism as anti-statism, thereby allowing other hierarchies to exist. This is similar to the narrow view that communists have towards the economy. Anti-statism is part of anarchism, but only a part of it. Anti-capitalism is part of anarchism, but only a part of it.