Funny question. It is precisely "to avoid Rutherford's problem". Bohr model consists of three postulates, which means that Bohr suggests it is like that. He assumes that it is like he says, without specifying why. He takes that as true, and then he derives his results.
Among the postulates, there are (from Wikipedia):
- Electrons in atoms orbit the nucleus.
- The electrons can only orbit
stably, without radiating, in certain orbits (called by Bohr the
"stationary orbits") at a certain discrete set of distances from
the nucleus. These orbits are associated with definite energies and
are also called energy shells or energy levels. In these orbits, the
electron's acceleration does not result in radiation and energy loss
as required by classical electromagnetics. The Bohr model of an atom
was based upon Planck's quantum theory of radiation.
And the thing is that Bohr's model did work reasonably well for the hidrogen atom.
Later on scientist discovered that things which worked were just a coincidence, and some other things were just wrong. However, it was probably a neccesary step in the way to QM.