Perhaps there is no science behind the way you do genealogy but there certainly is behind the way I carry out my research.
I study the reason behind the records I use to base my research on. I find out why they were created, what information is actually recorded, how it was recorded etc.
I also study the way the records have developed or changed throughout the centuries, both in what they record (and what they do not record) and how they are used.
When I have the information from the records I then experiment with the different combinations of that information to see if my theories hold water or if there are weaknesses in my assumptions. As I know many other genealogists do.
In the end I advance a theory; my tree which is the results of my research and experiments and is open to review by others to test, complying with another principle of science.
My tree is not fact, it is the collated results or my research based on a process of questioning the data recorded in the various historic records available. I do not try to prove the data to be true but try to prove the data to be false.
If I cannot prove the data to be false then I must accept it until further data comes to light.
Which if you look at the flow chart on the page you link to my methods fit very well into what is described there.
In fact that flow chart could actually describe genealogical research.
Definitions of Science
Oxford Dictionary:
The intellectual and practical activity encompassing the systematic study of the structure and behaviour of the physical and natural world through observation and experiment:
Cambridge Dictionary:
(knowledge from) the careful study of the structure and behaviour of the physical world, especially by watching, measuring, and doing experiments, and the development of theories to describe the results of these activities:
Note science does not provide proof of anything, science provides evidence or refutes evidence in exactly the way that good genealogical research does.
While we can't ever prove that a child inherits 50% of its DNA from each of its parents, experiment after experiment has shown this to be the case. The hypothesis has also been confirmed by empirical data from thousands of genetic genealogists who have tested themselves and their parents and see that they too inherit 50% of their DNA from each of their parents.
Whilst it is true that a child inherits 50% of their DNA from each parent it is not a simplistic as that. Much of the DNA a child inherits could come from either parent.
This means that after a couple of generations the DNA from one particular ancestor might no longer be found in the DNA of a person.
Science does not prove that one person is a parent but simply advances evidence that it is possible that a certain person could be the parent.
To say otherwise shows you do not understand the meaning of scientific research.
In fact I would go as far to say that to use DNA correctly one would have to not simply accept the analysed results of the DNA but question those results and try to prove them to be false.
But this part of science seems to be lost in your approach to DNA
Cheers
Guy