You don't know that his parents have 'loved and cared for him'. They could be toxic parents and the family could be dysfunctional. Just because they are famous and take nice photos together, and give nice interviews, it doesn't mean everything is great in private. What you see on camera can be gloss.
It's also not a 'private disagreement' if indeed his parents have been leaking twisted stories about his wife to the press via their agents.
FWIW I do think his parents love him
.. in as much as they're capable. But I also believe they love fame and love being brand Beckham....but ask the parents of many children who have gone no contact with them and many will also insist they love their children, and furthermore, say they cannot see what the estranged child's complaint is, because they gave them a good lifestyle.
Providing a rich lifestyle isn't the only thing of importance. Love involves protecting too. I think it's worth noting that many children whose lives are played out in the public eye, do not end up happy.
We don't know the truth of everything, but at the very least, BB seems to be saying his parents did not protect him. He grew up papped constantly and his family was a brand. The brand seems to have come first. The children's needs as individuals second. They did not seem to recognise his autonomy outside of the brand. They did not encourage him to find himself as a separate person, despite their huge wealth. His parents did not protect his emotional and mental health, and frankly I can believe that, as his words are typical of that spoken by people narrating their childhood experiences of growing up in Hollywood for e.g.
I also believe he's still being rather kind and reserved in this statement, because there have been (unsubstantiated) rumours about the Beckham's open marriage (supposedly only open on one side) for ages and he could have opened the full can. He's probably not done that because 1. He cares for his siblings 2. He still has some feeling for his parents. 3. His wife probably doesn't want him to go full nuclear.
This seems to me to be a bit of a 'back off and leave me and my wife alone' sort of statement in addition to correcting some untruths circulated by the Beckham's seemingly rather astute, protective and bolshy PR.
What a horrible position to be in. Most people with dysfunctional families get to sort out their emotions and the mental stress in private. He hasn't been afforded the luxury. I'm betting his parents will respond with the 'But we took you to stately homes' response.
But I agree that he may not come out of this well, since if the normal filial attachment isn't there from his parents then the Beckham's will use their PR to do damage limitations and they have a big fan base. It would be confirmatory that their brand is the most important thing to them in my opinion if they do that, but many would go along with it.