I suspect a fair number of the complainers are people with Democratic leanings, and I think I can describe their thought process to you.
I think their problem is that a private company is doing this, not the Government. Suppose someone has to be a caregiver for an elderly relative during COVID. Facebook probably won't offer them 10 weeks for paid leave for doing this, because Facebook's internal cost-benefit metrics tell them that it's not useful. That's why people are resentful – a private company should not be in charge of deciding who gets time to deal with changes as fundamental as this in society. Policies like Medicare for all, compulsory maternity and paternity leave, or caregiver leave implemented by the Government (ideally) take into account the wishes of society as a whole, not a large private company like Facebook. For example, I think caregiver leave would be very popular due to the aging population of the US being a large section of voters, there are already tax credits starting for the same thing.
I am personally fine with giving as much time as is needed for people with families as well as people in a bunch of other situations. Life is complex and we need to help out each other as much as possible. But I fear that the ruthless utilitarianism of most American corporations doesn't play well with this worldview, leading to resentments like the article describes.