In two-qubit system there are $ZZ$- and $XX$-interaction between the qubits, in some papers it is described how to remove such parasitic interactions, but I didn't find the reason of why does it happen?
This comes down very much to the physics of the individual devices. I'll describe here one relatively simple model which hopefully gives you a little bit of insight. But, as I say, it's different for each device...
Consider an optical lattice. You should basically think of a sinusoidal trapping potential. Within each minimum you could define a qubit by the presence or absence of an atom (there are better things to do, but I'm keeping it simple).
Now, whatever our best description of the wavefunction of the atom within a single potential well, that wavefunction extends outside that single well, and into the neighbouring ones. In other words, it has the possibility to tunnel from one potential well to the next. This would be described by a Hamiltonian $XX+YY$. You can even be precise about the coupling strength: simply ask what's the overlap between the wavefunction of an atom trapped in one site, with the wavefunction of an atom trapped in the next site. So, the higher you make the potential barrier between them, the smaller the overlap, and the smaller the coupling strength.