I remember hearing an individual on TV once - I believe he was on Charlie
Rose - and as I recall the argument goes something like this:

The European Americans did their utmost to exterminate Indian Culture on the
North American continent, from which the Indians never have, nor probably
ever will recover. What the Indians find offensive is that, as they see it,
the only thing we palefaces seem to value is their stereotype for aggression
as a symbol of our sports teams. (Building dioramas of Indian villages to
decorate casino lobbies doesn't count.)

This argument probably doesn't hold for the Irish, who have flourished in
modern times (granted after many decades of second class citizenship.)
Further, we value Irish culture; we drink Irish beverages, sing Irish songs,
listen to Irish tenors, read Irish literature, and every March 17th, we're
all Irish!! True, this is somewhat superficial, but it's more that what we
do for the culture of the aboriginal North Americans.

Note that this is not my argument, although I sympathize with it.
Interestingly enough, the guest on the show, a member of the Lakota tribe,
as I recall, said that the term "Native American" is not seen as an
improvement over "Indian". Among themselves the Indians refer to their
nation, e.g., "He's Lakota" or "She's Mahican".

Ken