Most of the time, this is not what the mother wants. Her partner has just been falsely arrested and so can't help with bills. She needs to make rent or she'll be evicted. She applies for assistance not to punish her partner, but to not be homeless with the children.
Even if you are innocent, you've just gone from being an employed, present Black dad...
To a dead beat dad, with warrants for his arrest for failure to pay child support, who can't even apply for many jobs due to the first arrest.