Quoted:
It shows the oscillation of the ice at the north pole as ongoing and changes very easily as it is floating over water. It also shows that the Antarctic Ice is growing quite rapidly.
And yet the extent of Arctic sea ice is in fact strongly down, is it not?
Antarctic sea ice extent is up. Antarctic land ice is in some trouble, though not as much as Greenland's.
OP, tell your neighbor that while she is right to be concerned, Greenland and Antarctica will take centuries or even millennia to melt.
The way this is portrayed to the useful idiots is that it is slowly melting away, when in fact it grows and shrinks with the seasons. Many animations show a ice cap shrinking into the summer months, but they don't show the rebound in winter. People ACTUALLY believe what they are being shown.
The graph on NSIDC's Arctic News page is February to February. The Arctic is melting away, though I would not agree with your characterization of it as slow. It's quite rapid.