Why is Turbo Tax forcing me to say that either I or my spouse paid more than half our home expenses when we split them equally?

Because you are claiming a dependent.   But why are you filing Joint?  You can still claim all the children both yours and spouse’s.  And you could be missing out on several credits.

Joint is almost always better.  Here's some things to consider about filing separately……

In the first place you each have to file a separate return, so that's two returns.  And if you are using the Online version that means using 2 accounts and paying the fees twice.  The Desktop CD/Download program would be better to use.

Many people think they come out better when filing Married Filing Separate but they are probably doing it wrong.  If one person itemizes deductions on Schedule A then the other one must itemize too, even if it's less than the standard deduction, even if it is ZERO!  And if you are in a Community Property state it can be complicated to figure out.

And there are several credits you can't take when filing separately, like the

EITC Earned Income Tax Credit

Child Care Credit

Educational Deductions and Credits

And contributions to IRA and ROTH IRA are limited when you file MFS.

Also if you file Married Filing Separately up to 85`% of your Social Security becomes taxable right away even with zero other income.

See …….

https://ttlc.intuit.com/community/married/help/is-it-better-for-a-married-couple-to-file-jointly-or-separately/00/25590

Which part of the return are you in?  Is this question where you are entering your dependent information?  If so, then if you each buy your own kids their clothes, or pay for your own children's school trips, etc, that person would pay more than half of the child's expenses. It is trying to determine who can claim the kids. To claim a qualifying child, they must get MORE than half of their support from you.  It must be more than 50% in order to claim certain credits.  So if you both claim 50%, neither person is technically paying MORE than half of the support.

Qualifying child

To qualify as a dependent, a child must also pass these tests:

• Relationship: Be your son, daughter, stepchild, eligible foster child, brother, sister, half-sister or -brother, stepbrother, stepsister, adopted child or the child of one of these
• Age: Be under age 19 or under 24 if a full-time student, or any age if permanently and totally disabled
• Residency: Live with you for more than half the year, with some exceptions
• Support: Get more than half their financial support from you
• Joint return: Not file as married filing jointly unless only to claim a refund of taxes paid or withheld