Answer:
   
   How could two people have two different, logically developed opinions
   on any issue? :-)
   
   In answering this, there are two important points to keep in mind:
     * Most decisions are not simply bilateral yes/no decisions
     * Valid interpretations according to traditional hermeneutics that
       differ in particulars of a particular place/time can survive
       concurrently (cf. any modern legal system)
       
   The Orthodox rabbis would both say that their halachic rulings are in
   line with the tradition of Torah learning, all the way from Sinai, and
   that their difference is in details. The Reform rabbi, however, might
   derive a ruling from other sources of morality, such as secular
   ethical notions of equality.
   
   Reform Rabbi Walter Jacob writes, in Contemporary American Reform
   Responsa that "Our path in America is clear and our halakhic stance is
   akin to the pluralism of the past from the days of Hillel and Shammai
   in the first century through the entire rabbinic period to our own
   time." Orthodox rabbis would counter that the schools of Hillel and
   Shammai differed on the particulars of halacha (with the understanding
   being that the multiplicity of debate was a byproduct of a disucssion
   of students, not disciples, resulting in flaws of transmission). Thus,
   the Orthodox scholars believe there was no disagreement over first
   principles, while Orthodox and Reform differ significantly on major
   principles, such as Torah being from G-d, and the authority of
   individuals to decide halacha for themselves.