"Finally, all of you, be like-minded, be sympathetic, love one another, be compassionate and humble." (1 Pet 3:18) .
It is so easy to fake compassion. Even a psychopath can fake feelings and love. Since compassion is usually known by the acts it performs... giving, caring; sometimes people could do those things without feeling any compassion at all.
They could be doing it for the glory or for a publicity stunt. Or even sometimes to shame the person they are helping. This is why I never cease to disapprove of the modern publicity of generosity by churches and individuals who would perform an act of kindness and pester it all over social media. Jesus condemned such act and so should we.
The real test of compassion is humility. The Bible says be compassionate and humble. If you are going to be compassionate make sure it is backed with humility and self denial.