Why is creating water exothermic? I have to calculate the bond dissociation energy of steam. I'm a total noob, so don't go too hard on me.
(I'm translating the exercise by myself, sorry if there is a mistake.)

Calculate the bond dissociation energy of gas-water/steam ($\ce{H2O}$). Whereas the total enthalpy of the bound is the sum of the &quot;sub-bounds&quot;. Use the following table:


Now, we have: $\ce{2H2 + O2 -&gt; 2H2O}$
Imagine we have a tank with one $\ce{O2}$ and two $\ce{H2}$, then, according to the table (if I read it correct), we need $2\cdot436\ \mathrm{kJ} + 497\ \mathrm{kJ}=1396\ \mathrm{kJ}$ to &quot;break&quot; the bonds. We then get two $\ce{O}$ and four $\ce{H}$. They react to two $\ce{H2O}$
Now, according to the table, two $\ce{H2O}$ need $2\cdot 2\cdot 463 \ \mathrm{kJ}=1852\ \mathrm{kJ}$ to bind together.
So, we start with a system of total inner energy $1396\ \rm kJ$ and end up with one of $1852\ \rm kJ$. Clearly, we have to put energy into the first system to get to the second.
Now, that's obviously false - but I don't get why. I'd expect a exothermic reaction because 1. I just know it is and 2. because the $\ce{O2}$ have a double bound which I just expect to be harder to break.
So where is my thought wrong?
You’re mistakenly conflating the bond dissociation energies between the diatomic components and the product molecule. If the bond dissociation energy of water is larger than the bond dissociation energy of the individual diatomic components, then the system is “lower energy” (preferred) in the $\ce{H2O}$ state and that “extra energy” in the atomic state will be released in the form of exothermic heating. Remember that elemental $\Delta H = 0$, and the water molecule has stronger bonds/lower enthalpy and would require more energy to dissociate than the elemental components (which is what your math shows), meaning water won’t spontaneously dissociate into the diatomic gases since that would be an endothermic process and require some external energy. As an aside, keep in mind that dissociation of bonds in a molecule like water won’t be consistent between atoms (after the first hydrogen bond has broken from an $\ce{H2O}$ molecule, the remaining hydroxyl group requires less energy to dissociate). In sum, if your product has a higher bond dissociation energy than your reactant, it’s at lower enthalpy and the net of the reaction will be a release of energy in the form of exothermic heating.