The Collaborative International Dictionary of English v.0.48:

Pair \Pair\, v. i. [imp. & p. p. Paired; p. pr. & vb. n.
   Pairing.]
   1. To be joined in pairs; to couple; to mate, as for
      breeding.
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   2. To suit; to fit, as a counterpart.
      [1913 Webster]

            My heart was made to fit and pair with thine.
                                                  --Rowe.
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   3. Same as To pair off. See phrase below.
      [1913 Webster]

   To pair off, to separate from a group in pairs or couples;
      specif. (Parliamentary Cant), to agree with one of the
      opposite party or opinion to abstain from voting on
      specified questions or issues. See Pair, n., 6.
      [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

Pairing \Pair"ing\, n. [See Pair, v. i.]
   1. The act or process of uniting or arranging in pairs or
      couples.
      [1913 Webster]

   2. See To pair off, under Pair, v. i.
      [1913 Webster]

   Pairing time, the time when birds or other animals pair.
      [1913 Webster]

WordNet (r) 3.0 (2006):

pairing
    n 1: the act of pairing a male and female for reproductive
         purposes; "the casual couplings of adolescents"; "the
         mating of some species occurs only in the spring" [syn:
         coupling, mating, pairing, conjugation, union,
         sexual union]
    2: the act of grouping things or people in pairs

Moby Thesaurus II by Grady Ward, 1.0:

67 Moby Thesaurus words for "pairing":
   Janus, agglomeration, agglutination, aggregation, ambiguity,
   ambivalence, articulation, biformity, bifurcation, bond,
   bracketing, clustering, combination, communication, concatenation,
   concourse, concurrence, confluence, congeries, conglomeration,
   conjugation, conjunction, connection, convergence, copulation,
   coupling, dichotomy, doubleness, doublethink, doubling, dualism,
   duality, duplexity, duplication, duplicity, equivocality,
   gathering, halving, hookup, intercommunication, intercourse,
   interlinking, irony, joinder, joining, jointure, junction,
   knotting, liaison, linkage, linking, marriage, meeting, merger,
   merging, polarity, splice, symbiosis, tie, tie-in, tie-up,
   twinning, two-facedness, twoness, unification, union, yoking