Step 1: Understanding the Concept:
The question asks for the central criticism of Thomas Malthus's population theory from Liberal and Marxist perspectives. Malthus argued that population grows geometrically while food supply grows arithmetically, leading to poverty and famine as natural outcomes of population outstripping resources.
Step 2: Detailed Explanation:
(A) That he disregarded poverty as a social problem: This is the core of the critique. Both Liberals and Marxists argue that poverty is not a 'natural' problem caused by population growth, but a social problem resulting from the unequal distribution of resources. Marx, in particular, argued that under capitalism, the system itself produces poverty and inequality, regardless of population numbers. Malthus was criticized for blaming the poor for their condition instead of blaming the economic structure.
(B) That he only talked about positive and preventive checks: This is a description of his theory, not a critique of it. Malthus did indeed discuss these checks.
(C) That he did not give a detailed theory of demographic transition: The theory of demographic transition was developed much later, so it's anachronistic to criticize Malthus for not detailing it.
(D) That he failed to give a theory of population explosion: On the contrary, his theory is one of the earliest theories of population explosion, describing the rapid growth of population when unchecked.
Step 3: Final Answer:
The fundamental critique from both Liberal and Marxist viewpoints is that Malthus incorrectly treated poverty as a natural consequence of population growth, thereby ignoring its social and economic roots in the unequal distribution of wealth.