If my dad passed away debt free without a Will and everything belongs to mom, do we have to probate and why?

I am so sorry for your loss.  If everything that was held by your Father was held jointly with your Mother then generally speaking, you do not have to probate his estate.  Everything would have passed "by operation of law" to your Mother at the death of your Father.  I am assuming that bank accounts were joint accounts and that real property (their home) was held with rights of survivorship.  There may be other assets that give rise to your asking this question so if there is something specific that makes you think you need to probate please seek legal help in your area.  Good luck.