How can you explain to your child why you did not raise them? I wish that there was a simple and satisfactory response to this question, but there is no easy answer. You take your time, consider carefully how your response might be received and do the best that you can. If you are a spiritual person, prayers are in order before you begin this conversation.
Although birth parents have some common reasons for placing a child for adoption, each situation is a bit different. There are many reasons for relinquishment, and some are better received by adoptees than others. Some adoptees are not terribly concerned about the reason. When a child is placed for adoption because the birth parents are extremly young and poor, that common scenario has the best chance of being considered a reason that an adoptee can comprehend and accept.
Understanding the logic behind the decision does not remove all the feelings about it, but it does help put the decision in perspective somewhat. Explanations are more difficult when the birth parents are older and have more financial resources. It might be harder for adoptees to understand the logic behind an adoption with this set of circumstances.
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When a rape is involved in an adoption, this too is a complicating factor. However difficult telling the truth about a rape might be, your child deserves to know this fact. This is particularly important if they are intent on locating their birth father.
Another complicating factor is when an affair is part of the adoption decision. You might be surprised how often an adoption is involved after an affair. Sometimes married couples are separated due to military service or other factors, and the woman becomes pregnant during their separation. If the couple intends to stay together, it is not uncommon for the man to insist on the adoption option.
Whatever the truth of an adoptee's story happens to be, they deserve to know their story. As a birth parent, you might be surprised to know what is included in the non-identifying information that they receive. They might already know more than you imagine.
Will it be hard to tell the honest truth? It might be, but you need to do it anyway. You also need to own up to your part in the decision as a birth parent. Even if you were coerced, your child might not consider you totally blameless. Tell the truth, no matter how hard it is. Some adoptees care deeply about your reasons, others are very blasé and it seems not to matter to them.