If you qualify for EIC the software will add it to your refund automatically. Why are you asking if you "have" to claim it?
Failure to claim the EIC when you qualify for it can also delay processing of the return since the IRS computers will pickup the missing form. Even if they don't now they will send a letter later. Then if you choose to amend the return that can take 4 months or more to process as well. So even if you could find a way around taking the EIC which will void the accuracy guarantee it would also require you to mail in the return which can also take months to process. Bottom line ... don't do it.
Now can you explain why you don't want the EIC ? Do you not qualify ?
You cannot forego the EIC to allow the other parent to claim the EIC, if the other parent is not qualified.
If you and the other parent live together, only one of you can claim the child for any tax benefit. The interview is confusing (it's designed for divorced parents, who are allowed to split the child). The second parent should not enter the child, at all.
There is a special rule in the case of divorced & separated (including never married) parents. When the non-custodial parent is claiming the child as a dependent/exemption/child tax credit; the custodial parent is still allowed to claim the same child for Earned Income Credit, Head of Household filing status, and day care credit. This "splitting of the child" is not available to parents who lived together at any time during the last 6 months of the year; then only one of you can claim the child for any tax reasons. The tax benefits may not be split in any other manner.
Note in particular that the non-custodial parent can never claim the Earned Income Credit, Head of Household filing status or the day care credit, based on that child, even when the custodial parent has released the dependency to him.