Many people in Florida hold their Social Security numbers very close and refuse to give them out unless there is no other option. They know that these numbers can be used for identity theft, so they want to limit exposure to protect themselves.
While this is wise, it's important to note that you have to provide your Social Security number if you are trying to establish paternity of a child who was born to you and your significant other while you were not married. In fact, you and your spouse both have to give over your Social Security numbers.
The need to do this was laid out in the Personal Responsibility and Work Opportunity Reconciliation Act of 1996. They can then be used along with the Title IV-D program.
So, what is the reason that the Social Security number is needed? Much of it has to do with work and income. The government wants to make sure that the parents both help pay to support the child. One parent may have custody and end up paying on a consistent basis as part of day-to-day life, but the other parent may also need to pay to compensate for the cost of care.
After all, one of the big reasons to establish paternity in the first place is to decide who is really the father of a child born out of wedlock, making it possible to then ask that father for support. Fatherhood is assumed within a marriage, but not without, even if the couple has been together for some time.
Both parties must be sure they know their rights and obligations regarding paternity and child support.
Source: Online Sunshine, "742.10 Establishment of paternity for children born out of wedlock.," accessed Nov. 13, 2015