Here's the actual sentence
"A subjective question begs a subjective answer..."
Something inside my head says it should have been
"A subjective question begs for a subjective answer..."
Which one is correct in that context?
Both are grammatical, but they mean different things. A subjective question begs a subjective answer means that such a question assumes a subjective answer. A subjective question begs for a subjective answer means it craves or entreats a subjective answer. However, there are potential hazards in putting beg and question in the same sentence at all. That is because some readers will insist that begging the question should only be used in the philosophical sense of petitio principii. Begging the answer isn’t the same thing as begging the question, but that won’t stop some people. You’d be much safer writing something like A subjective question prompts a subjective answer.