Someone asked me recently, "Are you sure that this person is the parent?"
Unless you have a parent/child DNA match, the answer to that question will always be "No." (Even if you do have a parent/child DNA match, the match could theoretically be your aunt/uncle, if your parent had an identical twin.)
DNA evidence by itself rarely constitutes genealogical proof, and the reason for that comes down to biology and human behavior.
A child always inherits 50% of its DNA from each parent. On average, a child inherits 25% of its DNA from each grandparent. In practice, however, a child can favor one grandparent's lineage more than the other. For example, a child may share 30% of its paternal grandfather's DNA but only 20% of its paternal grandmother's DNA.
Because DNA is randomized during meiosis, the process which creates egg and sperm cells, each child inherits a different combination of genetic material from its parents. This is why siblings may have different ethnicity percentages and may not closely resemble each other.
This variance can result in vastly different amounts of shared DNA for the same genealogical relationship. For example, third cousins may share 217 centimorgans (cM) of DNA or none at all.
According to Ancestry, you have a 98% chance of sharing a measurable DNA segment with a 3rd cousin. The probability drops to 71% for 4th cousins, 32% for 5th cousins, 11% for 6th cousins, and 3.2% for 7th cousins.
What does this mean for genealogy?
When searching for a distant relative, such as the parents of a brick wall ancestor, you will probably need access to multiple DNA kits and a chromosome browser. Each descendant of that ancestor may have inherited a different DNA segment from him or her (or none at all). Multiple DNA kits will increase your odds of finding a triangulated match that you can trace to a shared ancestor or location.
When searching for a biological parent, your closest DNA matches will typically be first or second cousins. However, they could also represent a variety of other relations (half-nephews, half-uncles, half-cousins, to name just a few), depending upon your age and family circumstances. It will be necessary to research and compare several DNA matches in order to understand how you are related. From there, it may be necessary to perform additional targeted DNA testing to identify your parent.
You also have to consider the possibility of misattributed parentage in your DNA matches. Even the most carefully documented family tree may not be genetically correct.
So how can I ever be sure?
It helps to have corroborating evidence. One person was given the hometown, surname, and approximate age of her birth mother, and she looked exactly like her proposed half-sister. Another person had family lore which linked him to his birth mother, and he also closely resembled his proposed half-siblings. Another person had his proposed grandfather's name on a baptismal record.
DNA can only take us so far. Without corroborating evidence, we may never be entirely sure.