In chapter 992 Marco and Perospero meet with Big Mom, and she affirms that she is allied with Kaido. Perospero accepts this while Marco realizes their interests aren’t mutual.
Big Mom questions Marco’s decision to aid the Straw Hats and implies he represents the remnants of Whitebeard’s crew in their entirety, but Marco counters by stating the former Whitebeard Pirates’ freedom to act individually. They aren’t bound by ‘the word of pops’ – the word of Whitebeard.
I think what Oda was really shining a light on here was the difference in ‘parenting’ style between Whitebeard and Big Mom, which reflects their respective moral character.
Whitebeard’s crew weren’t his biological children. Most of them were orphaned, or lost, and thus constituted a found family. Ace, the son Whitebeard gave his life to rescue, was in fact biologically the son of his greatest rival, Roger.
Whitebeard regarded his crew like children, raised and guided them, but didn’t force them to abide by his wishes. We know Ace went rogue in pursuit of Blackbeard, a sin for which Whitebeard ultimately paid the price. When Oden chose to join Roger, Whitebeard, despite his anger, didn’t stand in Oden’s way.
This contrasts pretty strongly with Big Mom, whose crew consists almost entirely of her true biological children, forced to live and act as she desires. So Big Mom’s assumption that Marco’s actions are somehow representative of Whitebeard’s wishes is a reflection of her values.
Perospero and her other children want to see her become Pirate King – but they didn’t really have much choice in that matter. Where Whitebeard’s crew chose to call themselves ‘sons’ of Whitebeard when they joined his crew, Big Mom’s children are forced into servitude from birth.