What is the Biblical basis against the existence of one "ideal" spouse for each person? What is a Biblical rebuttal of the belief that there is one right person (a soulmate) to be your spouse?
Finding the Right Spouse Not Really Biblical

The history of marriage in the Bible seems to provide little basis for the idea that we must find "the one right person in the entire world."  Abraham remarried after Sarah died and, as the saying goes, "had many sons".  Abraham's servant chose a bride for Isaac, so Isaac certainly had no opportunity to find the right one for him.  Jacob actually chose one and ended up getting the one he wanted and another one he didn't want (or expect).  

A problem with the idea of "the one right person in the entire world" is that more often than we would like, tragedy strikes and a spouse dies.  That leads to the surviving spouse finding another "one right person in the entire world," who presumably was not the "one right person in the entire world" while the other "one right person in the world" was living.

Finding the Right Kind of Person

There is, however, good reason to seek "the right kind" of spouse.  The passage about being "equally yoked" is often quoted to support the idea that believer should not marry unbelievers.  It would seem, however, that the verse is broader than marriage and broader than just believer to unbeliever.  A large discrepancy in the commitment level of two people to Christ could certainly be problematic.  One person who is deeply committed to Christ could probably experience a lot of grief if the spouse prioritizes other things over church and such things as that.


  Do not be unequally yoked with unbelievers. For what partnership has
  righteousness with lawlessness? Or what fellowship has light with
  darkness?  2 Corinthians 6:14 ESV


So, it is wise to look for a godly person with integrity and honor who is emotionally healthy, not selfish, who you would be friends with even if you weren't married to them.

Be the Right Person

The Bible actually gives a lot of instructions, not about finding the right spouse, but about being the right spouse.  Husbands are commanded to love their wives sacrificially, as Christ modeled in His sacrifice for the church.  Wives are urged to respect their husbands.  


  25 Husbands, love your wives, as Christ loved the church and gave
  himself up for her, 26 that he might sanctify her, having cleansed her
  by the washing of water with the word, 27 so that he might present the
  church to himself in splendor, without spot or wrinkle or any such
  thing, that she might be holy and without blemish.[a] 28 In the same
  way husbands should love their wives as their own bodies. He who loves
  his wife loves himself. 29 For no one ever hated his own flesh, but
  nourishes and cherishes it, just as Christ does the church, 30 because
  we are members of his body. 31 “Therefore a man shall leave his father
  and mother and hold fast to his wife, and the two shall become one
  flesh.” 32 This mystery is profound, and I am saying that it refers to
  Christ and the church. 33 However, let each one of you love his wife
  as himself, and let the wife see that she respects her husband.  Ephesians 5:25-33 ESV


We are not accountable for the life and actions of others, but we are, indeed, accountable for our own lives and actions.  So, we are responsible to become the person God calls us to be.

We should each seek to become a caring, servant-minded, giving, humble, honorable, faithful, godly person of integrity and honor--not just try to find someone like that to marry who then has to put up with us for the rest of their lives.