Earlier quoted context omitted.
I Am Not An Immunologist, but antibodies are usually produced by plasma cells, after their predecessor B cells are triggered with the appropriate antigens, right? I'm pretty sure that mechanism and its memory is acquired, not innate. In other words, it's not coded for by DNA, and you can't inherit that immunity from the father. Some maternal antibodies are heritable, but I think that's through shared blood.
For 'Not An Immunologist' you seem to have a pretty good handle on this stuff. You're mostly right about the heritability stuff, but it's a bit more subtle than that. Antibodies are built from heavy and light chains, which are in turn produced by a combinatorial recombination process: subunits get spliced together. While paternal B cells aren't going anywhere with regards to heritability, the heavy/light chain subuni…
Haha, maybe I should get go get an immunology text. I think I'm pushing the limits of Wikipedia.