How the ABO system works
ABO blood type is decided by a single gene with three possible versions: IA, IB and i. IA and IB are codominant with each other — which is why type AB exists, carrying both at once — and both dominate over i, the version that gives type O.
That means someone with type A can have genotype IAIA or IAi, and the two look identical from the outside: the only way to tell which is by looking at their parents or children. That is why two type-A parents can have, with no genetic surprise involved, a type-O child: if both are hidden carriers of i, the i+i combination gives type O.
What IS a settled fact: impossible types
Even though a type-A or type-B parent's exact genotype cannot be known, it IS possible to know with certainty which types a child can NEVER have. Two type-O parents, for instance, can only pass on the i allele: their child will always be type O, with no exception possible within ordinary ABO genetics.
Here is the full table of what is possible — the same one blood banks use: O×O → O only. O×A → O or A. O×B → O or B. O×AB → A or B (never O or AB). A×A → O or A. B×B → O or B. A×B → any of the four types. A×AB → A, B or AB. B×AB → A, B or AB. AB×AB → A, B or AB (never O).
The Rh factor
Rh is a separate gene from ABO: Rh+ is dominant over Rh−. Two Rh− parents can only have Rh− children, no exception. But if one or both are Rh+, the child can come out Rh+ or Rh−, because an Rh+ parent can carry a hidden Rh− copy without it showing from the outside — the same hidden-genotype issue as with ABO.
It matters for pregnancy for a real medical reason: when the mother is Rh− and the baby is Rh+, the mother's immune system can react against the baby's blood in later pregnancies if left untreated. That is why every Rh− pregnant woman routinely receives an anti-D immunoglobulin injection — a standard part of prenatal care, not a warning sign.
About the 'this blood can't be from this father' myth
This worry circulates a lot and almost always comes from not knowing the table above: seeing a type-O child with a type-A father looks odd until you know that A×A can also produce O. Blood type can only EXCLUDE parentage with certainty — if the child's type is not on the list of possibilities for both parents — never confirm it: matching the table is compatible with a huge number of people, and proves nothing on its own.
If your child's result comes out as impossible on this calculator and there is no typing error involved, that is worth raising with a professional — not something to resolve on your own. The overwhelming majority of the time, the surprise is simply explained by not knowing one parent's hidden genotype.