The phrase suggests an emotional disconnect or lack of compassion towards someone or something. Despite her pleas, I was out of sympathy with her situation after repeated dishonesty.
Pro Tip 2/3
Support Withdrawal
Use the phrase to indicate that you no longer support a cause or person you previously might have. After learning about the scandal, many became out of sympathy with the politician.
Pro Tip 3/3
Not Just Disagree
It's stronger than just not agreeing; it suggests an active opposition or disapproval. She was out of sympathy with the new policy, actively campaigning for its repeal.