how do electrical arcs occur?
You can read about arc furnaces here. The first thing you might notice is that your description only applies to small furnaces.


  A mid-sized modern steelmaking furnace would have a transformer rated
  about 60,000,000 volt-amperes (60 MVA), with a secondary voltage
  between 400 and 900 volts and a secondary current in excess of 44,000
  amperes.


However, even 400 to 900 volts is not enough to produce an arc over any reasonable distance, so your question remains valid. And the article supplies the answer:


  The electrodes are lowered onto the scrap, an arc is struck


In other words, the electrodes make direct contact with the metal to be melted, so voltage is pretty much irrelevant as long as it produces adequate current. In fact,


  Lower voltages are selected for this first part of the operation to
  protect the roof and walls from excessive heat and damage from the
  arcs. Once the electrodes have reached the heavy melt at the base of
  the furnace and the arcs are shielded by the scrap, the voltage can be
  increased and the electrodes raised slightly, lengthening the arcs and
  increasing power to the melt.