Should you refuse to show compassion because you believe it would make you appear weak, then you have misunderstood what strength is. It is honorable to have concern for others, to show empathy and to offer aid to someone in distress. To rebuke this is cowardice, not strength.
THIS. Willie showed no concern about my health after I put two dozen eggs in the microwave and it inexplicably exploded. NO. It was all 'don't do that ALF' and 'microwaves cost money ALF'. WELL SO DOES MY NOSE!!!