Varieties of criticism
Conservative criticism has nothing much to do with "left-wing" or "right-wing", because left-wing people are often very conservative, in the defined sense, while right-wing people can also be very radical, in the defined sense. The difference between "radical" and "conservative" has more to do with the belief in whether "a change to something genuinely new" is really possible and necessary. Radicals typically believe strongly that such change is highly desirable and necessary, and that it can be achieved. Their criticism is that there is "not enough" change. Conservative critics, by contrast, are very skeptical about any such change, because they feel the change is really "just another form" of something that already exists.
Left-wing politics
Left-wing politics supports social equality and egalitarianism, often in opposition to social hierarchy. It typically involves a concern for those in society whom its adherents perceive as disadvantaged relative to others (prioritarianism) as well as a belief that there are unjustified inequalities that need to be reduced or abolished (by advocating for social justice). The term left-wing can also refer to "the radical, reforming, or socialist section of a political party or system".