Looking at the remark in context, we can see what Caranthir is trying to say.
The context is that the Noldor have recently exiled themselves from Aman and returned to Middle-earth, to take the Silmarils from Morgoth. On arrival, they have already fought one major battle and Fëanor has died. They have realised, overlate, that they cannot defeat Morgoth (or at least that it won't be easy). So they have settled in for the long haul.
The Sons of Fëanor look down on the Sindar. They feel that the Sindar, not being Elves of the Light (i.e. never having seen the Two Trees), are inferior to the Noldor. And of course, as happens again and again, the Oath of Fëanor makes them make foolish decisions - they see whatever they want as the most important thing. So they expect their King Thingol to be grateful to them for having at least forced Morgoth back in battle. In particular, they expect to be able to form kingdoms of their own in the territory of Beleriand.
Not surprisingly Thingol is not so keen on this idea. He does not see why he should grant large chunks of his kingdom to the new arrivals from the West.
Now Angrod, like Caranthir, is a grandson of Finwë, so he is also a Noldo. But his mother was not a Noldo. The book says:
Alone of the princes of the Noldor those of Finarfin's [Angrod's father] house were suffered to pass within the confines of Doriath; for they could claim close kinship with King Thingol himself, since their mother was Eärwen of Alqualondë, Olwë's daughter [so she is Thingol's niece].
So Angrod, quite reasonably went to Thingol, as he was allowed to, and spoke diplomatically to the King. Thingol gave the Noldor permission to live in empty regions. But Caranthir is angry at him, because he is proud and unreasonable - he feels that the Exiles should be able to take whatever they want.
So he says that Angrod has gone over to the other side. He refers to Thingol contemptuously as "a Dark Elf in a cave" (which is false - Thingol has seen the Light of the Two Trees!). He says that Angrod has forgotten his father (who is a Noldo) and remembers only his mother (who is Thingol's niece). Of course he does not mean that Angrod has literally forgotten his father, only that Angrod is (he says) putting his mother's family over his father's.