Given his CS contribution it doesn't look like the X in this case IS earning a packet. In the UK non-resident parents pay 25% of their weekly earnings over 100GBP in CSA for a first child (the more kids they have the less money they pay per child), and that amount is reduced by 13% for every overnight they have the child. Only the richest of non-resident parents actually ends up paying 50% of a child's real-life expenses on that system. He couldn't choose not to pay anyway, the courts garnish wages in the UK if the father doesn't pay. He would have to drop out of DD's life altogether and move away and then never work to not pay (they find people through their national insurance number which comes onto the tax system whenever one works) and if he did that i'd consider it his loss.
I'm not saying she has no right to be angry about it, but i do think that 6 years of refusal to pay for Primary education is a pretty clear indication that he isn't going to pay for her education. And i think the decisions you make when you're a couple, as a couple, hold far less water once you break up. That's one reason i asked if he had talked about Catholic school recently. I'll be pretty mad if XP starts reminding me of potential financial commitments i made nearly a decade back when DD is 10. On the other hand i'll be pretty pi$$ed off if he decides a week after agreeing that he will that he'd actually rather not pay for something.
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