Question about claiming children on taxes

My ex is saying that if he starts paying child support, that it is only fair that he claim one of the 2 children on next year’s tax returns. Can you tell me the rationale for why the custodial parent claims the children, even when they are receiving child support from the non-custodial parent? I know this is how it works, but I’m having trouble justifying this to him.

No. The IRS rules state that the parent with whom the children are residing has the right to claim them, as they are the ones who provide for all the daily needs.