While I certainly agree that there is no honor in "suffering with", I
think the word "compassion" has a useful referent not inconsistent with
its etymology and usage here: "to desire that others not suffer."
That's a simple value judgment, and I think a completely rational one.
Rather than "suffering with", which accomplishes nothing, to desire the
end of others' suffering is a prerequisite of acting to end it. And
ending others' suffering is a rational act for several reasons: e.g.,
sufferers not productive traders. Some suffering is precipitated by--
I hesitate to say caused because suffering itself is choice--genuine
misfortune, and learning how to end suffering can teach us how to deal
with those misfortunes.
That in particular is one of the quite valid criticisms of Rand: that
she willfully evades the reality that success is often as much a product
of blind luck as it is of work. While a rational man would not suffer
faced with such misfortune, many others do, and desiring to end their
suffering can have valuable consequences.