Is it wrong?

[MTL]

Personally, I'd worry more about the mental health of people who can't pick up a newspaper without crumbling over the obituaries (as they might, if, for example, one belonged their mother).  That, to me, would indicate a problem.  That would seem strange.  We're made of tougher shit than that, we've been dealing with death for far too long for that to be an appropriate or well adjusted response.

Yes, and even an Empathetic person can choose  to be detached if needs must, at least sometimes.

It is also worth noting that while many people, even those with a relatively normal degree of Empathy,
just shake their head over mass shootings in the news, and then move on with their day;

one story over another might move you to tears,
and you might not even necessarily know why;

(And I can also bawl my eyes out over a tearjerker of a movie,
even if I know it is 100% fiction).

I have to steel myself, quite deliberately, over stories of animal cruelty, for example.

I CAN do it, but it takes a conscious decision;
and I only do so out of necessity
...when I am obliged to stay focused on something urgent.

Also:  I feel oddly guilty when I do so, as well
...as if, by allowing myself to feel grief,
I share in and somehow diminish the animal's suffering

...which, of course, is nonsense.

I think that stems from the same social instinct that makes people feel OBLIGED to "not give up" on someone,
or to hold out "hope" for a missing person for a protracted period of time,
as opposed to simply WANTING for things to work out;

somehow we feel guilty for giving up hope,
even though holding out hope for an extended period of time can be exhausting
...as if we think by giving up hope,
we are somehow withdrawing the only support the missing person might have, or something.