It’s the difference between how we act these days, and how they acted back then.
We now differentiate between “biological” parents and “adoptive” parents.
Adoption, back then, was understood differently. The adopted child actually *became *a part of the family - i.e. body and blood. The family’s ancestors became his. He could claim them as his ancestors, without qualifying it as we do nowadays by saying “by adoption” or “my step-grandmother.”
In fact, part of that still operates today - an adopted child has the same legal rights as a legitimate biological child. A child born out of wedlock to a married man doesn’t have as many legal rights as that man’s adopted child. The adopted child is the legal next of kin; the illegitimate one isn’t, unless formally adopted by its father! If a man dies without a will, his legitimate and adopted children automatically inherit. His illegitimate children do not. (See the scandal sheets for many examples of an illegitimate child suing over inheritances.)
So, when Joseph married Mary, Jesus *became *his son, and a descendant of Joseph’s ancestors.
Hope this helps.
God bless you,
Ruthie