To be more specific, Jung's psychology has been characterized as "unscientific" on the following grounds:
that some Jungian concepts, such as archetypes and synchronicity, cannot be proven by the scientific method
that Jung subscribed to a nineteenth-century notion of evolution that has since been discredited
that Jung's valuation of the mental functions of feeling and intuition on the same level as thinking weakens the attitude of rational objectivity that is essential in scientific research
that Jung's interest in occult traditions, including the pre-scientific European past (third-century Gnosticism and medieval alchemy) and contemporary Asian cultures (Taoism and Tibetan Buddhism) amounts to a glorification of mysticism and irrationality
that Jung's clinical specialization in the treatment of schizophrenia and his own brush with psychosis made him an untrustworthy guide to "ordinary" reality
how do you feel about who has the burden of proof? the person claiming the thing or someone saying there is no evidence to suggest that the claim is correct?