I agree. Fair doesn't mean biassed.
There ought to be an investigation. The senate should call witnesses. Each of the parties should be interviewed. From those witness accounts and the interviews of the parties, people should draw their conclusions.
That's a fair scenario, as best as can be had. If K appears innocent, so be it. So far, his actions look less trustworthy than hers to me. Getting coaching to answer these allegations is another granule adding to my sense that K isn't a candid candidate.
It sounds to me like he may have lied about a drunken escapade as a 17 year old. If so, the lie now makes him more culpable than the actions then. Then, at least, he was young and drunk. Now he's an adult, a judge and a parent.
I suspect his life has been the sort in which he hasn't had to learn many tough lessons. And so essentially he hasn't really grown as a person. Stepping aside may make him the person he could be. Better to be a good person than a tainted justice.