I have changed the practice area to family law, so lawyers in that area can respond. The answer is that the court wasn't claiming contempt, the person put in jail was in contempt. Child support is not just a debt, it is a court ordered requirement. There are many safeguards in place to prevent if from becoming debtor's prison. If, for example, the person cannot pay for some reason, then assuming they prove that, the judge will not throw them in jail. But if they just spend their money on other things, then the judge will not have much sympathy. And is someone doesn't pay child support and does not get a lawyer to present the matter to the judge, then they are bound to lose. If I were a judge, and someone came to me before they were in arrears, I would listen, but if they just didn't pay and then try to make excuses when they were brought to court on contempt, I probably would not believe them.
This is not legal advice. You should always discuss the specifics of your issue in person with an attorney. Be aware that there are time limits on all claims that depend on the kind of claim, so do not delay in seeking an attorney.