It's so much more than just feelings of betrayal and feeling like fool, Renata. If you're a good parent, you will devote much of your time and resources to raising a child. You will have set aside much of your personal desires and rearrange your life in order to make room for them.
If you have a good family, your children will become an inseparable part it. Extended family, grandparent, aunts, uncles and cousins cultivate lasting relationships with your children.
Now, let's say, after 13 years, you discover that they aren't your children, they are someone else's. Of course you still love them, but that relationship has been tainted. They will be a constant reminder of that betrayal. It not only affects you but every member of your extended family. Their extended family will see them differently. The damage done to the children is arguably even worse.
There is also a good chance that your opportunity to raise your own biological children has passed, or you simply do not have the resources. None of this has been by your choice. You've been tricked into it.
I feel very confident that my children are mine, because of how they were conceived. My wife and I got married before we had children and she told me she wanted to start trying to have each of them. She came home when conception was most likely and said: “Tonights the night! Let’s make baby.” However, if my children did one of the ancestry tests (like 23andme), and they found out I was not the father, I don’t know if I would want to know. It would be devastating. If my wife had an affair, I think I could live with that. I would be heart broken, but I could recover. That’s different then finding out my children aren’t mine. I don’t think I explain it and I don’t think most women will ever understand what it means, either. If they did, the wouldn’t get offended at the idea of paternity tests.