That there are things in experience that depend on a person or individual, such as tastes, appreciations, and feelings of many kinds seems fairly to very evident, as is the opposite thesis and term objective, that stands for what is given in one's experience that does not or not much depend on a person's or individual's tastes, feelings, values or desires. (Note that what may seem objective, and thus may seem to be really there, may be mostly intersubjective.)

The problems are often how to draw the line between what individuals experience of and about something, and what they have contributed to their sensations from their own resources, whether beliefs, desires, memories or fantasies, and what is really there, apart from human or animal belief, guess, feeling, need or indeed existence.

Two good examples of the opposition subjective/objective concern respectively probability and ethics.

In probability theory it has been argued, e.g. by Ramsey, De Finetti and Savage, that there is a very fundamental sense in which probabilistic judgements in which probabilities are assigned to propositions are subjective, even if the calculus of probabilities that prescribes how to calculate with these probabilities is the same for all, and is indeed a branch of (mathematical) measure theory.

One problem here is that, if that is so, as seems indeed at least plausible for the bets people place on horses and the like, that even if they are based on some evidence tend to be mostly based on subjective feelings or considerations, to what extent this subjectiveness would hold for or extend to probability in general.

Some, like De Finetti, have argued that there is nothing but subjective assessments of basic probabilities coupled to a mathematical axiomatic theory of measurement; others have argued that there really are indeterministic processes and chances in nature, and also many kinds of empirical events that may be  sampled and that behave objectively as described by the mathematics of probability, regardless of human subjective notions or feelings, and regardless of sampling or the quality of the samples.

In ethics it has been argued, e.g. by Russell and Edwards, that all ethical judgments are in the end subjective, and not really based on either the nature of things, or the desires or presciptions of a God (or the authorities).

One problem here is that, if that is so, there seems to be no objective basis whatsoever to ethical judgments, and that thus it would be a mere matter of subjective taste whether this or that person will be burned alive or not, about which ultimately little can said or argued except "de gustibus non disputandum".