Formation of zwitterion from amino acids
The reason amino acids exist largely in their zwitterionic form at biological $\mathrm{pH}$ (usually around 7) is due to the $\mathrm{p}K_\mathrm{a}$ of the constituent groups. It's not that the oxygen 'wants' to lose a proton, but more that at that $\mathrm{pH}$ the equilibrium lies towards the deprotonated state (things are rarely 100% protonated/deprotonated). 

In general, carboxylic acids easily lose their proton to form carboxylates (the anionic charge is delocalised over the three atoms making the proton loss 'favourable'), and amines act as bases, to pick up a proton. 

At a $\mathrm{pH}$ of 7, the medium is basic enough to cause the carboxylic acid to be deprotonated, and the amine to be protonated. If you look at the diagram below, you can see that increasing or decreasing the pecan shift the equilibrium towards fully protonated (at low $\mathrm{pH}$) or fully deprotonated (at high $\mathrm{pH}$) amino acid. 



Ionisation state of amino acids over 0-14 $\mathrm{pH}$ range, taken from Biochemistry, Berg (7 ed.)