As the difficulty for creating sane biological taxonomies indicates, the real world does not lend itself to such artificial simplicity. (Extinction of the duck-billed platypus might help, but I'd miss the little guys -- and besides that, I can't give birth to live young myself, so I'm obviously not a mammal.)
The duck-billed platypus is a monotreme, an ancient relative of mammals. Before we knew about genes, one might think that it was part duck and part beaver, but we know about genes now, and therefore better understand evolution. It's pretty straightforward to fit it into a phylogeny, and horizontal gene transfer has nothing to do with it. I agree that single inheritance is a crappy way to design software, but this is a bad example.