Your understanding before wasn't quite right. The ionizing in ionizing radiation is the key, its about knocking off an electron to form an ion. So that's something like a UV photon exciting an electron and breaking a covalent chemical bond. Hydrogen bonds are weaker electrostatic interactions between molecules where the charge is distributed in two molecules such that they have a weak + and - charge arrangement. So pure water for example, the hydrogens from one molecule have a bit more + and the oxygen has a bit more - within each molecule. If you think about how that works with a bunch of magnets fixed on a peg board they all try and match up their N and S if you move one they all wobble around to find a new arrangement to minimise the energy across the board. Thats hydrogen bonding all the H and O between different molecules try and match their charges. In DNA there are either 2 or 3 of those kinds of bonds to match up. Covalent bonds are more like how the magnets are fixed on the peg board. So if you split a magnet off its way more chaos right? That magnet will fly off and stick to another one and all bets are off on how everything else will interact.