Why is this named 3-phenyl-2-butanol instead of 2-phenyl-3-butanol?
You have already correctly identified the compound as a phenylbutanol. The only remaining problem is the numbering of locants. The most important simplified criteria for the numbering in such cases are:


lower locants for the principal characteristic group that is expressed as suffix
lower locants for multiple bonds (first to double bonds if there is a choice)
lower locants for prefixes
lower locants for substituents cited first as a prefix in the name


The corresponding actual wording in the current version of Nomenclature of Organic Chemistry – IUPAC Recommendations and Preferred Names 2013 (Blue Book) reads as follows:


  P-14.4 NUMBERING
  
  When several structural features appear in cyclic and acyclic compounds, low locants are assigned to them in the following decreasing order of seniority:
  
  (…)
  
  (c) principal characteristic groups and free valences (suffixes);
  
  (…)
  
  (e) saturation/unsaturation:
  
    (i) low locants are given to hydro/dehydro prefixes (…) and ‘ene’ and ‘yne’ endings;
  
    (ii) low locants are given first to multiple bonds as a set and then to double bonds (…);
  
  (f) detachable alphabetized prefixes, all considered together in a series of increasing numerical order;
  
  (g) lowest locants for the substituent cited first as a prefix in the name;
  
  (…)


Clearly, the $\ce{-OH}$ group is the principal characteristic group in this case since you have already used it as principal characteristic group to find the correct suffix ‘ol’.

Therefore, a low locant is assigned first to the $\ce{-OH}$ group according to Rule (c), which yields phenylbutan-2-ol.

After that, a low locant is assigned to the phenyl group according to Rule (f); however, the only possible numbering left is 3-phenylbutan-2-ol.