Why is tantalum so unreactive?
I think the answer to your question can be described based primarily on thermodynamic considerations.  Ta has very high fusion (25 kJ/mol), vaporization (760 kJ/mol) and atomization (780 kJ/mol) enthalpies which are a result of strong metal-metal bonding in the solid (see Greenwood and Earnshaw, Chemistry of the Elements).  

To further understand the protective nature of the native oxide that forms on Ta, it is fruitful to look at an Ellingham diagram, which describes the stability of a metal oxide as a function of temperature. For more authoritative sources than the Wikipedia page, see a comprehensive Inorganic Chemistry textbook such as those by Shriver and Atkins or Housecroft and Sharpe.  I found this site particularly interesting for purposes of visualizing Ellingham diagrams and used it to make the following plot:



(Apologies for the color scheme, which was not adjustable)

Here I've plotted the free energy for the oxide formation of tantalum oxide along with oxides of iron and aluminum.  The x-axis is temperature.  The large negative values for each of these oxides indicates that they are all thermodynamically favorable at the temperatures plotted.  Room temperature would be very slightly to the left of the intersection of the x and y-axes.  A complete analysis of the stability of the metal oxides would also require consideration of kinetics, but we can use thermodynamics to postulate that the very large negative values for the free energy of formation of the tantalum oxide are one factor in the stability of the oxide film.  I'll leave it to the OP to play around with thermochemical cycles, which should demonstrate why the oxide films are resistant to many types of acids.