You see rand is actually trans-gender, The pattern saw that as a male he could not win, the male source would just be tainted again, so it bound his soul with a woman's before he was born (my guess is lanfear, it explains how she can always access his dreams, she is part of him). This gave him access to both parts of the pattern, then it brought him and moridin together so know all three are bound and only rand (being the center of that binding) gets access to all three parts of power.

p.s. no I don't really believe that at all but i always wanted to have a crazy theory that was way out there.