Why don't the "child" peptide masses sum to the parent in this De novo sequencing example?
In a peptide tandem mass spectrometry experiment, each fragment (child) ion is typically the result of breaking a single bond in the peptide backbone yield b and y ions. Because each ion fragment ion is the result of one fragmentation event, we don't expect the fragment ion masses to sum to the precursor mass.
If your peptide was fragmented well, you should get a ladder of b and y ions where the differences in masses between ions in the b and y ion series correspond to the masses of amino acids (+/- any modifications and neutral losses, such as the NH3 and H2O mentioned above).
A great resource for understanding these concepts is this tutorial:
https://www.ionsource.com/tutorial/DeNovo/introduction.htm