Thanks everyone for that brilliant discussion of why "strong woman" is repellent, I have thought so for years.
Sorry to go on when it's all been done so well by you lot, but also:
there is the tone of surprise - the person saying it is often congratulating themselves for recognising strength in a woman, thereby showing that they are wise and tolerant and filled with love and awe for the mystery that is womanhood;
men who speak of "strong women" in their family are often thinking they will impress you by doing this, as you are a feminist, so you will adore them for having and recognising a "strong woman" for a mother or sister. However, as HereBeBex says, this is often a euphemism for having been crapped on by men chronically and systematically for many years, not only without actually dying, but still holding things together for those they love, that is: for the very man who is trying right now to use this fact to sell himself to you as a mate. So in other words what he is saying is: my dad treated my mum like shit, drank and gambled all the money, my mum fainted with hunger several times in my childhood while putting food on the table for me, aren't women great, in fact better than men, and when we are together I will behave like an irresponsible entitled brat and you will uncomplainingly work and keep house and feed me and the kids, because women are Strong.
Those two points are about people describing other people as Strong Women. Women who do it themselves are .... oh, don't start me.