insensitive

Expressing or feeling little or no concern, care, compassion, or consideration for the feelings, emotions, sentiments, or concerns of other people; inconsiderate or incompassionate.

Not expressing normal physical feeling.

It is something like the way dame Nature gathers round a foreign body an envelope of some insensitive tissue which can protect from evil that which it would otherwise harm by contact.

Not expressing normal emotional feelings; cold; tactless; undiplomatic.

1895, Grant Allen, The British Barbarians Somehow, when Bertram Ingledew let it once be felt he did not wish to be questioned on any particular point, even women managed to restrain their curiosity: and he would have been either a very bold or a very insensitive man who would have ventured to continue questioning him any further.

Oh I really should have known by the time you drove me home, / By the vagueness in your eyes, your casual good-byes, / By the chill in your embrace and the expression on your face, / That told me you might have some advice to give / On how to be insensitive.