If he is the father and they all live together, no form is required. Those questions can be confusing. Either one of them can claim the child without filing an 8332. When you get to the question about an agreement, answer NO. That form is for couples that live apart.
But what really concerns me is why they would be filing separately. That sounds like really bad advice as Married Filing Separately is the worst filing status, especially when a child is involved. I would check that because if they have been filing MFS for years now, they may have forgone a lot of credits. They can still amend some returns if needed.
The main reason you'd want to file separately is to protect yourself from inaccurate tax information reported by your spouse, or in cases where your spouse refuses to file a joint return (or refuses to file period) and you don't want to get in trouble.
Generally, filing jointly will give you a bigger refund or fewer taxes due. When you file separately, your tax rate is higher and you won't be able to claim:
On top of that, if you live in the community property states of Arizona, California, Idaho, Louisiana, Nevada, New Mexico, Texas, Washington, or Wisconsin, you have to deal with community property allocations and adjustments, which adds extra work and complexity to your tax preparation chores.
Tip: Only taxpayers who were still legally married as of December 31, 2020, are able to file as married, whether jointly or separately.
Filing jointly means you file one tax return. When filing separately, you file two tax returns and pay double.
Want to compare filing jointly vs. separately?
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