I watched it last night again.
I think there's enough subtext there to suggest Silva is her illegitimate son. We'll never know, though, and it doesn't even matter -- because the reality is that the relationship (between her and Bond, and between her and Silva) DOES reflect a mother/son relationship whether it's blood or not.
They were both betrayed by M; Silva was traded for a number of spies, Bond was traded for the hard disk (which Moneypenny failed to retrieve). Their lives were expendable. M used them.
So Silva's the son that felt betrayed and went bad; Bond also was betrayed, but he never turns on Mum. It's definitely a replacement of the bad son with the good son.
Silva goes bad because of the betrayal, while Bond forgives her / sees the rationale of her choices, and also accepts his own complicity in them... ("You know I made the right call, and you would have too") and even though Bond continues to snipe with her, you know he understands her decision and approves. He knows he's a tool... yet a willing one. And he actually loves her; she really is his family/mother, after he was orphaned so many years prior. She disciplines him when he gets out of line and never pulls punches, yet she also believes in him (and this is actually the thing that seems to have riled him most when she ordered Eve to take the shot earlier in the movie -- not that she risked killing him, but that she did not believe he could get the drive and the shot was even necessary).
So the big deal is that Silva saw her trading him as a "sellout of him" and a breaking of trust, and he tries to get Bond to view her sending him back to the field despite his failing the tests as yet another expendient abuse of an old broken tool... but Bond never sees it that way, he sees it as her choice to believe in him again despite his failing the tests.