Not sure if this aligns with what the GP was trying to say, but this is also one of the groups I would expect to be the most depressed, although I would expect white, middle-aged, middle-classed women to be an even larger demographic. Chemicals/genetics have a lot to do with depression, but for other cases I think depression comes from a feeling of uselessness/lack of purpose.
White liberal women have a lot of incompatible expectations placed on them. If they stay home to raise children, they're labeled as lazy, "betraying the feminist cause", etc. for not participating in the workforce. If they work, they're labeled as neglectful of their children (if they have them) or told they're going to regret their choices. They have to outpace their male coworkers to be respected at work, but their career is also seen as a "nice to have". So the standards for women are impossible, but simultaneously so low that achieving them doesn't earn respect.
In a strange way, the group's relative privilege is a contributing factor to depression. If you're a member of a group that is violently oppressed, the act of protest and standing up to oppressors provides a sense of purpose. Because white women's position isn't "that bad," though, attempts to improve their situation are considered too small to celebrate at best and entitled whining at worse. Further, there's been a movement, particularly in liberal spaces over the past few years, to lift up the voices of the most oppressed. So liberal white women have pressure to just shut up and swallow their concerns from both sides of the political aisle.
None of this is to advocate drowning out the concerns of other groups to prioritize the mental health of white women, only a recognition that a seemingly easier life doesn't necessarily mean a happier one. In fact, an easier life can be more depressing.