It is not surprising to hear that an ex with Borderline traits has quickly moved on to a new relationship. Possibly it involves a pattern called "object constancy" which, to some extent, could be compared to "out of sight, out of mind". (Object constancy was a phrase used in my Custody Evaluator's recommendation report, though he never once named a specific mental health dysfunction.)
A reasonably normal person would not be so quick. We would need some time for closure, to assess what had happened and adjust (recover) to the new life situation. That also is why we advise our members to give ourselves time to recover, regain our equilibrium and resist jumping into "rebound" relationships.
Your distress that he didn't consider your feelings by jumping so quickly to another is understandable... and also predictable. Logic and reasoning you try would typically fail. Your ex's thinking is prone to lean more toward self-oriented perceptions and thinking, not normalcy such as empathy or compassion. Over on our
Tool & Skills Workshops board we have a topic that discusses why our attempts at JADE (Justify, Argue, Defend, Explain) so easily fail.
Due to the often-intractable nature of BPD, unless there are children that require continuing contact for parenting communication, many have had to go LC/MC (low contact, medium chill) or even NC (no contact). There are variable circumstances - including the extent of the BPD traits - that impact such decisions but generally we have to Gift ourselves Closure.