An ancient saying, no doubt, passed down through the ages. You see most families usually at each other's throats with countless issues, fighting and sniping against each other for years and years. If blood is thicker than water, it's not apparent in most families these days. But there usually is a bond in most families that keeps them together, through love, sacrifice, support of each other and familiarity. Genetics are at the core of all families...but by no means the crux, the center, the it of families. You can have non-genetically related people as friends, who can share the same love and bond as families-but there's not one ounce of blood between them.
A lot of deep friendships are formed out of trust, support and sacrifice. Many friends have gone out of their way to help each other, sometimes even sacrificing their own lives to save their friends. Families are formed out of genetics, through generations, but everybody who knows anybody long enough have exactly the same problems as any family, because in a sense they are a 'family'. Families are at the nexus of our society, generations come and go, but blood may be physically thicker than water due to the oxygen-rich hemoglobin and corpuscles...not necessarily just out of, and entirely of genetics. The same bonds can exist anywhere there is a complex relationship between more than one person.
If blood were thicker than water, at times I wouldn't feel like punching my quote, unquote 'idiot' brother out from time to time...I think most of us siblings believe that. It doesn't diminish the reality that he's my brother and that I feel some kind of bond between us going back to childhood. But in no way does it mean that 'blood is thicker than water'. With parents, they create and nurture life-and are fairly bonded to their children. But it's out a deep love and bonding from creating those children from their very essence. A mother bonds to her child because she carries that life inside her body, becomes totally responsible for that life, brings it into the world, nurturing it along the way into young adulthood, as her mom did with her, and so forth and so forth along through the generations. In part, developing through complex patterns through the evolution of humanity and the higher areas of the human brain, that all humans have gone through.
A better way of phrasing 'Blood is thicker than water' is 'Blood and water can be equal in viscosity, and can be separated at times with various mean differences'. Families are bonded together through the evolution of them over thousands of generations, coming from ancient clans and tribes that stood together, fought together, and died together. There are also many adopted children who are raised with the same love and affection as biological children. Their parents never see them as any less as their children, and may actually see them as far more because they were adopted, in part from empathy. But in most part from love, affection and kindness, all from the higher-centers of the human brain.
There are widows and widowers with children and marry each other. Their children become stepbrothers and stepsisters to each other, usually never even noticing the blood difference. There are also many half-brothers and sisters, who never see themselves as any less, and also may see themselves as more because they are out of the traditional boundaries of full-genetics in families and don't feel the same type of evolutionary constraints as families. In some cases, they may even have stronger relationships because they are not fully bonded through tribal and clan ways.
Most times, they even have better sibling-relationships with each other than full-biological siblings because the automatic genetic-link is not always used as a standard. They expand their relationship in a profound way that respects their respective parents coming together, their sibling relationship, but transcends the lack of common genetics in a deep, loving, very intense way. Families are indeed the heart of our society and that fact will never go away. But a standard is not necessary to exemplify that fact...they exist everywhere there is a human connection. As human beings, we are all connected together, one way or another.