That American Academy of Pediatrics sums up most of the cons against private cord banking nicely in their subject review of cord blood banking, in which they state that 'Families may be vulnerable to emotional marketing at the time of birth of a child and may look to their physicians for advice. No accurate estimates exist of the likelihood of children to need their own stored cells. The range of available estimates is from 1:1000 to 1:200,000. Empirical evidence that children will need their own cord blood for future use is lacking. There also is no evidence of the safety or effectiveness of autologous cord blood transplantation for the treatment of malignant neoplasms. For these reasons, it is difficult to recommend that parents store their children's cord blood for future use.'
Also keep in mind that the AAP again, in a 2007 policy statement on cord blood banking titled Cord Blood Banking for Potential Future Transplantation, stated that 'private storage of cord blood as "biological insurance" should be discouraged.'
Also, if your child does get one of the conditions that an umbilical cord transplant is supposed to cure or treat, if you don't store your child's cord blood, that doesn't mean that no treatments will be available to him. In addition to more traditional treatments and bone marrow transplants, you may be able to find a cord blood match in a public cord blood bank, from which most cord blood transplants are currently being done.
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